diff --git a/README.md b/README.md
index a43918464..e7a6e955b 100644
--- a/README.md
+++ b/README.md
@@ -2241,12 +2241,12 @@ Run from the repository root:
 import asyncio
 
 from mcp import ClientSession
-from mcp.client.streamable_http import streamablehttp_client
+from mcp.client.streamable_http import streamable_http_client
 
 
 async def main():
     # Connect to a streamable HTTP server
-    async with streamablehttp_client("http://localhost:8000/mcp") as (
+    async with streamable_http_client("http://localhost:8000/mcp") as (
         read_stream,
         write_stream,
         _,
@@ -2370,11 +2370,12 @@ cd to the `examples/snippets` directory and run:
 import asyncio
 from urllib.parse import parse_qs, urlparse
 
+import httpx
 from pydantic import AnyUrl
 
 from mcp import ClientSession
 from mcp.client.auth import OAuthClientProvider, TokenStorage
-from mcp.client.streamable_http import streamablehttp_client
+from mcp.client.streamable_http import streamable_http_client
 from mcp.shared.auth import OAuthClientInformationFull, OAuthClientMetadata, OAuthToken
 
 
@@ -2428,15 +2429,16 @@ async def main():
         callback_handler=handle_callback,
     )
 
-    async with streamablehttp_client("http://localhost:8001/mcp", auth=oauth_auth) as (read, write, _):
-        async with ClientSession(read, write) as session:
-            await session.initialize()
+    async with httpx.AsyncClient(auth=oauth_auth, follow_redirects=True) as custom_client:
+        async with streamable_http_client("http://localhost:8001/mcp", http_client=custom_client) as (read, write, _):
+            async with ClientSession(read, write) as session:
+                await session.initialize()
 
-            tools = await session.list_tools()
-            print(f"Available tools: {[tool.name for tool in tools.tools]}")
+                tools = await session.list_tools()
+                print(f"Available tools: {[tool.name for tool in tools.tools]}")
 
-            resources = await session.list_resources()
-            print(f"Available resources: {[r.uri for r in resources.resources]}")
+                resources = await session.list_resources()
+                print(f"Available resources: {[r.uri for r in resources.resources]}")
 
 
 def run():
diff --git a/examples/clients/simple-auth-client/mcp_simple_auth_client/main.py b/examples/clients/simple-auth-client/mcp_simple_auth_client/main.py
index 38dc5a916..a88c4ea6b 100644
--- a/examples/clients/simple-auth-client/mcp_simple_auth_client/main.py
+++ b/examples/clients/simple-auth-client/mcp_simple_auth_client/main.py
@@ -11,15 +11,15 @@
 import threading
 import time
 import webbrowser
-from datetime import timedelta
 from http.server import BaseHTTPRequestHandler, HTTPServer
 from typing import Any
 from urllib.parse import parse_qs, urlparse
 
+import httpx
 from mcp.client.auth import OAuthClientProvider, TokenStorage
 from mcp.client.session import ClientSession
 from mcp.client.sse import sse_client
-from mcp.client.streamable_http import streamablehttp_client
+from mcp.client.streamable_http import streamable_http_client
 from mcp.shared.auth import OAuthClientInformationFull, OAuthClientMetadata, OAuthToken
 
 
@@ -193,7 +193,7 @@ async def _default_redirect_handler(authorization_url: str) -> None:
             # Create OAuth authentication handler using the new interface
             # Use client_metadata_url to enable CIMD when the server supports it
             oauth_auth = OAuthClientProvider(
-                server_url=self.server_url,
+                server_url=self.server_url.replace("/mcp", ""),
                 client_metadata=OAuthClientMetadata.model_validate(client_metadata_dict),
                 storage=InMemoryTokenStorage(),
                 redirect_handler=_default_redirect_handler,
@@ -212,12 +212,12 @@ async def _default_redirect_handler(authorization_url: str) -> None:
                     await self._run_session(read_stream, write_stream, None)
             else:
                 print("📡 Opening StreamableHTTP transport connection with auth...")
-                async with streamablehttp_client(
-                    url=self.server_url,
-                    auth=oauth_auth,
-                    timeout=timedelta(seconds=60),
-                ) as (read_stream, write_stream, get_session_id):
-                    await self._run_session(read_stream, write_stream, get_session_id)
+                async with httpx.AsyncClient(auth=oauth_auth, follow_redirects=True) as custom_client:
+                    async with streamable_http_client(
+                        url=self.server_url,
+                        http_client=custom_client,
+                    ) as (read_stream, write_stream, get_session_id):
+                        await self._run_session(read_stream, write_stream, get_session_id)
 
         except Exception as e:
             print(f"❌ Failed to connect: {e}")
diff --git a/examples/snippets/clients/oauth_client.py b/examples/snippets/clients/oauth_client.py
index 45026590a..140b38aed 100644
--- a/examples/snippets/clients/oauth_client.py
+++ b/examples/snippets/clients/oauth_client.py
@@ -10,11 +10,12 @@
 import asyncio
 from urllib.parse import parse_qs, urlparse
 
+import httpx
 from pydantic import AnyUrl
 
 from mcp import ClientSession
 from mcp.client.auth import OAuthClientProvider, TokenStorage
-from mcp.client.streamable_http import streamablehttp_client
+from mcp.client.streamable_http import streamable_http_client
 from mcp.shared.auth import OAuthClientInformationFull, OAuthClientMetadata, OAuthToken
 
 
@@ -68,15 +69,16 @@ async def main():
         callback_handler=handle_callback,
     )
 
-    async with streamablehttp_client("http://localhost:8001/mcp", auth=oauth_auth) as (read, write, _):
-        async with ClientSession(read, write) as session:
-            await session.initialize()
+    async with httpx.AsyncClient(auth=oauth_auth, follow_redirects=True) as custom_client:
+        async with streamable_http_client("http://localhost:8001/mcp", http_client=custom_client) as (read, write, _):
+            async with ClientSession(read, write) as session:
+                await session.initialize()
 
-            tools = await session.list_tools()
-            print(f"Available tools: {[tool.name for tool in tools.tools]}")
+                tools = await session.list_tools()
+                print(f"Available tools: {[tool.name for tool in tools.tools]}")
 
-            resources = await session.list_resources()
-            print(f"Available resources: {[r.uri for r in resources.resources]}")
+                resources = await session.list_resources()
+                print(f"Available resources: {[r.uri for r in resources.resources]}")
 
 
 def run():
diff --git a/examples/snippets/clients/streamable_basic.py b/examples/snippets/clients/streamable_basic.py
index 108439613..071ea8155 100644
--- a/examples/snippets/clients/streamable_basic.py
+++ b/examples/snippets/clients/streamable_basic.py
@@ -6,12 +6,12 @@
 import asyncio
 
 from mcp import ClientSession
-from mcp.client.streamable_http import streamablehttp_client
+from mcp.client.streamable_http import streamable_http_client
 
 
 async def main():
     # Connect to a streamable HTTP server
-    async with streamablehttp_client("http://localhost:8000/mcp") as (
+    async with streamable_http_client("http://localhost:8000/mcp") as (
         read_stream,
         write_stream,
         _,
diff --git a/src/mcp/client/session_group.py b/src/mcp/client/session_group.py
index da45923e2..f82677d27 100644
--- a/src/mcp/client/session_group.py
+++ b/src/mcp/client/session_group.py
@@ -17,6 +17,7 @@
 from typing import Any, TypeAlias, overload
 
 import anyio
+import httpx
 from pydantic import BaseModel
 from typing_extensions import Self, deprecated
 
@@ -25,7 +26,8 @@
 from mcp.client.session import ElicitationFnT, ListRootsFnT, LoggingFnT, MessageHandlerFnT, SamplingFnT
 from mcp.client.sse import sse_client
 from mcp.client.stdio import StdioServerParameters
-from mcp.client.streamable_http import streamablehttp_client
+from mcp.client.streamable_http import streamable_http_client
+from mcp.shared._httpx_utils import create_mcp_http_client
 from mcp.shared.exceptions import McpError
 from mcp.shared.session import ProgressFnT
 
@@ -47,7 +49,7 @@ class SseServerParameters(BaseModel):
 
 
 class StreamableHttpParameters(BaseModel):
-    """Parameters for intializing a streamablehttp_client."""
+    """Parameters for intializing a streamable_http_client."""
 
     # The endpoint URL.
     url: str
@@ -309,11 +311,18 @@ async def _establish_session(
                 )
                 read, write = await session_stack.enter_async_context(client)
             else:
-                client = streamablehttp_client(
-                    url=server_params.url,
+                httpx_client = create_mcp_http_client(
                     headers=server_params.headers,
-                    timeout=server_params.timeout,
-                    sse_read_timeout=server_params.sse_read_timeout,
+                    timeout=httpx.Timeout(
+                        server_params.timeout.total_seconds(),
+                        read=server_params.sse_read_timeout.total_seconds(),
+                    ),
+                )
+                await session_stack.enter_async_context(httpx_client)
+
+                client = streamable_http_client(
+                    url=server_params.url,
+                    http_client=httpx_client,
                     terminate_on_close=server_params.terminate_on_close,
                 )
                 read, write, _ = await session_stack.enter_async_context(client)
diff --git a/src/mcp/client/streamable_http.py b/src/mcp/client/streamable_http.py
index fa0524e6e..ed28fcc27 100644
--- a/src/mcp/client/streamable_http.py
+++ b/src/mcp/client/streamable_http.py
@@ -6,19 +6,26 @@
 and session management.
 """
 
+import contextlib
 import logging
 from collections.abc import AsyncGenerator, Awaitable, Callable
 from contextlib import asynccontextmanager
 from dataclasses import dataclass
 from datetime import timedelta
+from typing import Any, overload
+from warnings import warn
 
 import anyio
 import httpx
 from anyio.abc import TaskGroup
 from anyio.streams.memory import MemoryObjectReceiveStream, MemoryObjectSendStream
 from httpx_sse import EventSource, ServerSentEvent, aconnect_sse
+from typing_extensions import deprecated
 
-from mcp.shared._httpx_utils import McpHttpClientFactory, create_mcp_http_client
+from mcp.shared._httpx_utils import (
+    McpHttpClientFactory,
+    create_mcp_http_client,
+)
 from mcp.shared.message import ClientMessageMetadata, SessionMessage
 from mcp.types import (
     ErrorData,
@@ -53,6 +60,9 @@
 JSON = "application/json"
 SSE = "text/event-stream"
 
+# Sentinel value for detecting unset optional parameters
+_UNSET = object()
+
 
 class StreamableHTTPError(Exception):
     """Base exception for StreamableHTTP transport errors."""
@@ -67,17 +77,25 @@ class RequestContext:
     """Context for a request operation."""
 
     client: httpx.AsyncClient
-    headers: dict[str, str]
     session_id: str | None
     session_message: SessionMessage
     metadata: ClientMessageMetadata | None
     read_stream_writer: StreamWriter
-    sse_read_timeout: float
+    headers: dict[str, str] | None = None  # Deprecated - no longer used
+    sse_read_timeout: float | None = None  # Deprecated - no longer used
 
 
 class StreamableHTTPTransport:
     """StreamableHTTP client transport implementation."""
 
+    @overload
+    def __init__(self, url: str) -> None: ...
+
+    @overload
+    @deprecated(
+        "Parameters headers, timeout, sse_read_timeout, and auth are deprecated. "
+        "Configure these on the httpx.AsyncClient instead."
+    )
     def __init__(
         self,
         url: str,
@@ -85,6 +103,15 @@ def __init__(
         timeout: float | timedelta = 30,
         sse_read_timeout: float | timedelta = 60 * 5,
         auth: httpx.Auth | None = None,
+    ) -> None: ...
+
+    def __init__(
+        self,
+        url: str,
+        headers: Any = _UNSET,
+        timeout: Any = _UNSET,
+        sse_read_timeout: Any = _UNSET,
+        auth: Any = _UNSET,
     ) -> None:
         """Initialize the StreamableHTTP transport.
 
@@ -95,24 +122,40 @@ def __init__(
             sse_read_timeout: Timeout for SSE read operations.
             auth: Optional HTTPX authentication handler.
         """
+        # Check for deprecated parameters and issue runtime warning
+        deprecated_params: list[str] = []
+        if headers is not _UNSET:
+            deprecated_params.append("headers")
+        if timeout is not _UNSET:
+            deprecated_params.append("timeout")
+        if sse_read_timeout is not _UNSET:
+            deprecated_params.append("sse_read_timeout")
+        if auth is not _UNSET:
+            deprecated_params.append("auth")
+
+        if deprecated_params:
+            warn(
+                f"Parameters {', '.join(deprecated_params)} are deprecated and will be ignored. "
+                "Configure these on the httpx.AsyncClient instead.",
+                DeprecationWarning,
+                stacklevel=2,
+            )
+
         self.url = url
-        self.headers = headers or {}
-        self.timeout = timeout.total_seconds() if isinstance(timeout, timedelta) else timeout
-        self.sse_read_timeout = (
-            sse_read_timeout.total_seconds() if isinstance(sse_read_timeout, timedelta) else sse_read_timeout
-        )
-        self.auth = auth
         self.session_id = None
         self.protocol_version = None
-        self.request_headers = {
-            ACCEPT: f"{JSON}, {SSE}",
-            CONTENT_TYPE: JSON,
-            **self.headers,
-        }
-
-    def _prepare_request_headers(self, base_headers: dict[str, str]) -> dict[str, str]:
-        """Update headers with session ID and protocol version if available."""
-        headers = base_headers.copy()
+
+    def _prepare_headers(self) -> dict[str, str]:
+        """Build MCP-specific request headers.
+
+        These headers will be merged with the httpx.AsyncClient's default headers,
+        with these MCP-specific headers taking precedence.
+        """
+        headers: dict[str, str] = {}
+        # Add MCP protocol headers
+        headers[ACCEPT] = f"{JSON}, {SSE}"
+        headers[CONTENT_TYPE] = JSON
+        # Add session headers if available
         if self.session_id:
             headers[MCP_SESSION_ID] = self.session_id
         if self.protocol_version:
@@ -216,7 +259,7 @@ async def handle_get_stream(
                 if not self.session_id:
                     return
 
-                headers = self._prepare_request_headers(self.request_headers)
+                headers = self._prepare_headers()
                 if last_event_id:
                     headers[LAST_EVENT_ID] = last_event_id  # pragma: no cover
 
@@ -225,7 +268,6 @@ async def handle_get_stream(
                     "GET",
                     self.url,
                     headers=headers,
-                    timeout=httpx.Timeout(self.timeout, read=self.sse_read_timeout),
                 ) as event_source:
                     event_source.response.raise_for_status()
                     logger.debug("GET SSE connection established")
@@ -258,7 +300,7 @@ async def handle_get_stream(
 
     async def _handle_resumption_request(self, ctx: RequestContext) -> None:
         """Handle a resumption request using GET with SSE."""
-        headers = self._prepare_request_headers(ctx.headers)
+        headers = self._prepare_headers()
         if ctx.metadata and ctx.metadata.resumption_token:
             headers[LAST_EVENT_ID] = ctx.metadata.resumption_token
         else:
@@ -274,7 +316,6 @@ async def _handle_resumption_request(self, ctx: RequestContext) -> None:
             "GET",
             self.url,
             headers=headers,
-            timeout=httpx.Timeout(self.timeout, read=self.sse_read_timeout),
         ) as event_source:
             event_source.response.raise_for_status()
             logger.debug("Resumption GET SSE connection established")
@@ -292,7 +333,7 @@ async def _handle_resumption_request(self, ctx: RequestContext) -> None:
 
     async def _handle_post_request(self, ctx: RequestContext) -> None:
         """Handle a POST request with response processing."""
-        headers = self._prepare_request_headers(ctx.headers)
+        headers = self._prepare_headers()
         message = ctx.session_message.message
         is_initialization = self._is_initialization_request(message)
 
@@ -410,7 +451,7 @@ async def _handle_reconnection(
         delay_ms = retry_interval_ms if retry_interval_ms is not None else DEFAULT_RECONNECTION_DELAY_MS
         await anyio.sleep(delay_ms / 1000.0)
 
-        headers = self._prepare_request_headers(ctx.headers)
+        headers = self._prepare_headers()
         headers[LAST_EVENT_ID] = last_event_id
 
         # Extract original request ID to map responses
@@ -424,7 +465,6 @@ async def _handle_reconnection(
                 "GET",
                 self.url,
                 headers=headers,
-                timeout=httpx.Timeout(self.timeout, read=self.sse_read_timeout),
             ) as event_source:
                 event_source.response.raise_for_status()
                 logger.info("Reconnected to SSE stream")
@@ -512,12 +552,10 @@ async def post_writer(
 
                     ctx = RequestContext(
                         client=client,
-                        headers=self.request_headers,
                         session_id=self.session_id,
                         session_message=session_message,
                         metadata=metadata,
                         read_stream_writer=read_stream_writer,
-                        sse_read_timeout=self.sse_read_timeout,
                     )
 
                     async def handle_request_async():
@@ -544,7 +582,7 @@ async def terminate_session(self, client: httpx.AsyncClient) -> None:  # pragma:
             return
 
         try:
-            headers = self._prepare_request_headers(self.request_headers)
+            headers = self._prepare_headers()
             response = await client.delete(self.url, headers=headers)
 
             if response.status_code == 405:
@@ -560,14 +598,11 @@ def get_session_id(self) -> str | None:
 
 
 @asynccontextmanager
-async def streamablehttp_client(
+async def streamable_http_client(
     url: str,
-    headers: dict[str, str] | None = None,
-    timeout: float | timedelta = 30,
-    sse_read_timeout: float | timedelta = 60 * 5,
+    *,
+    http_client: httpx.AsyncClient | None = None,
     terminate_on_close: bool = True,
-    httpx_client_factory: McpHttpClientFactory = create_mcp_http_client,
-    auth: httpx.Auth | None = None,
 ) -> AsyncGenerator[
     tuple[
         MemoryObjectReceiveStream[SessionMessage | Exception],
@@ -579,30 +614,45 @@ async def streamablehttp_client(
     """
     Client transport for StreamableHTTP.
 
-    `sse_read_timeout` determines how long (in seconds) the client will wait for a new
-    event before disconnecting. All other HTTP operations are controlled by `timeout`.
+    Args:
+        url: The MCP server endpoint URL.
+        http_client: Optional pre-configured httpx.AsyncClient. If None, a default
+            client with recommended MCP timeouts will be created. To configure headers,
+            authentication, or other HTTP settings, create an httpx.AsyncClient and pass it here.
+        terminate_on_close: If True, send a DELETE request to terminate the session
+            when the context exits.
 
     Yields:
         Tuple containing:
             - read_stream: Stream for reading messages from the server
             - write_stream: Stream for sending messages to the server
             - get_session_id_callback: Function to retrieve the current session ID
-    """
-    transport = StreamableHTTPTransport(url, headers, timeout, sse_read_timeout, auth)
 
+    Example:
+        See examples/snippets/clients/ for usage patterns.
+    """
     read_stream_writer, read_stream = anyio.create_memory_object_stream[SessionMessage | Exception](0)
     write_stream, write_stream_reader = anyio.create_memory_object_stream[SessionMessage](0)
 
+    # Determine if we need to create and manage the client
+    client_provided = http_client is not None
+    client = http_client
+
+    if client is None:
+        # Create default client with recommended MCP timeouts
+        client = create_mcp_http_client()
+
+    transport = StreamableHTTPTransport(url)
+
     async with anyio.create_task_group() as tg:
         try:
             logger.debug(f"Connecting to StreamableHTTP endpoint: {url}")
 
-            async with httpx_client_factory(
-                headers=transport.request_headers,
-                timeout=httpx.Timeout(transport.timeout, read=transport.sse_read_timeout),
-                auth=transport.auth,
-            ) as client:
-                # Define callbacks that need access to tg
+            async with contextlib.AsyncExitStack() as stack:
+                # Only manage client lifecycle if we created it
+                if not client_provided:
+                    await stack.enter_async_context(client)
+
                 def start_get_stream() -> None:
                     tg.start_soon(transport.handle_get_stream, client, read_stream_writer)
 
@@ -629,3 +679,44 @@ def start_get_stream() -> None:
         finally:
             await read_stream_writer.aclose()
             await write_stream.aclose()
+
+
+@asynccontextmanager
+@deprecated("Use `streamable_http_client` instead.")
+async def streamablehttp_client(
+    url: str,
+    headers: dict[str, str] | None = None,
+    timeout: float | timedelta = 30,
+    sse_read_timeout: float | timedelta = 60 * 5,
+    terminate_on_close: bool = True,
+    httpx_client_factory: McpHttpClientFactory = create_mcp_http_client,
+    auth: httpx.Auth | None = None,
+) -> AsyncGenerator[
+    tuple[
+        MemoryObjectReceiveStream[SessionMessage | Exception],
+        MemoryObjectSendStream[SessionMessage],
+        GetSessionIdCallback,
+    ],
+    None,
+]:
+    # Convert timeout parameters
+    timeout_seconds = timeout.total_seconds() if isinstance(timeout, timedelta) else timeout
+    sse_read_timeout_seconds = (
+        sse_read_timeout.total_seconds() if isinstance(sse_read_timeout, timedelta) else sse_read_timeout
+    )
+
+    # Create httpx client using the factory with old-style parameters
+    client = httpx_client_factory(
+        headers=headers,
+        timeout=httpx.Timeout(timeout_seconds, read=sse_read_timeout_seconds),
+        auth=auth,
+    )
+
+    # Manage client lifecycle since we created it
+    async with client:
+        async with streamable_http_client(
+            url,
+            http_client=client,
+            terminate_on_close=terminate_on_close,
+        ) as streams:
+            yield streams
diff --git a/src/mcp/shared/_httpx_utils.py b/src/mcp/shared/_httpx_utils.py
index 3af64ad1e..945ef8095 100644
--- a/src/mcp/shared/_httpx_utils.py
+++ b/src/mcp/shared/_httpx_utils.py
@@ -4,7 +4,11 @@
 
 import httpx
 
-__all__ = ["create_mcp_http_client"]
+__all__ = ["create_mcp_http_client", "MCP_DEFAULT_TIMEOUT", "MCP_DEFAULT_SSE_READ_TIMEOUT"]
+
+# Default MCP timeout configuration
+MCP_DEFAULT_TIMEOUT = 30.0  # General operations (seconds)
+MCP_DEFAULT_SSE_READ_TIMEOUT = 300.0  # SSE streams - 5 minutes (seconds)
 
 
 class McpHttpClientFactory(Protocol):  # pragma: no branch
@@ -68,7 +72,7 @@ def create_mcp_http_client(
 
     # Handle timeout
     if timeout is None:
-        kwargs["timeout"] = httpx.Timeout(30.0)
+        kwargs["timeout"] = httpx.Timeout(MCP_DEFAULT_TIMEOUT, read=MCP_DEFAULT_SSE_READ_TIMEOUT)
     else:
         kwargs["timeout"] = timeout
 
diff --git a/tests/client/test_http_unicode.py b/tests/client/test_http_unicode.py
index 95e01ce57..ec38f3583 100644
--- a/tests/client/test_http_unicode.py
+++ b/tests/client/test_http_unicode.py
@@ -12,7 +12,7 @@
 import pytest
 
 from mcp.client.session import ClientSession
-from mcp.client.streamable_http import streamablehttp_client
+from mcp.client.streamable_http import streamable_http_client
 from tests.test_helpers import wait_for_server
 
 # Test constants with various Unicode characters
@@ -178,7 +178,7 @@ async def test_streamable_http_client_unicode_tool_call(running_unicode_server:
     base_url = running_unicode_server
     endpoint_url = f"{base_url}/mcp"
 
-    async with streamablehttp_client(endpoint_url) as (read_stream, write_stream, _get_session_id):
+    async with streamable_http_client(endpoint_url) as (read_stream, write_stream, _get_session_id):
         async with ClientSession(read_stream, write_stream) as session:
             await session.initialize()
 
@@ -210,7 +210,7 @@ async def test_streamable_http_client_unicode_prompts(running_unicode_server: st
     base_url = running_unicode_server
     endpoint_url = f"{base_url}/mcp"
 
-    async with streamablehttp_client(endpoint_url) as (read_stream, write_stream, _get_session_id):
+    async with streamable_http_client(endpoint_url) as (read_stream, write_stream, _get_session_id):
         async with ClientSession(read_stream, write_stream) as session:
             await session.initialize()
 
diff --git a/tests/client/test_notification_response.py b/tests/client/test_notification_response.py
index 19d537400..7500abee7 100644
--- a/tests/client/test_notification_response.py
+++ b/tests/client/test_notification_response.py
@@ -18,7 +18,7 @@
 from starlette.routing import Route
 
 from mcp import ClientSession, types
-from mcp.client.streamable_http import streamablehttp_client
+from mcp.client.streamable_http import streamable_http_client
 from mcp.shared.session import RequestResponder
 from mcp.types import ClientNotification, RootsListChangedNotification
 from tests.test_helpers import wait_for_server
@@ -127,7 +127,7 @@ async def message_handler(  # pragma: no cover
         if isinstance(message, Exception):
             returned_exception = message
 
-    async with streamablehttp_client(server_url) as (read_stream, write_stream, _):
+    async with streamable_http_client(server_url) as (read_stream, write_stream, _):
         async with ClientSession(
             read_stream,
             write_stream,
diff --git a/tests/client/test_session_group.py b/tests/client/test_session_group.py
index e61ea572b..755c613d9 100644
--- a/tests/client/test_session_group.py
+++ b/tests/client/test_session_group.py
@@ -280,7 +280,7 @@ async def test_disconnect_non_existent_server(self):
             (
                 StreamableHttpParameters(url="http://test.com/stream", terminate_on_close=False),
                 "streamablehttp",
-                "mcp.client.session_group.streamablehttp_client",
+                "mcp.client.session_group.streamable_http_client",
             ),  # url, headers, timeout, sse_read_timeout, terminate_on_close
         ],
     )
@@ -296,7 +296,7 @@ async def test_establish_session_parameterized(
                 mock_read_stream = mock.AsyncMock(name=f"{client_type_name}Read")
                 mock_write_stream = mock.AsyncMock(name=f"{client_type_name}Write")
 
-                # streamablehttp_client's __aenter__ returns three values
+                # streamable_http_client's __aenter__ returns three values
                 if client_type_name == "streamablehttp":
                     mock_extra_stream_val = mock.AsyncMock(name="StreamableExtra")
                     mock_client_cm_instance.__aenter__.return_value = (
@@ -354,13 +354,14 @@ async def test_establish_session_parameterized(
                     )
                 elif client_type_name == "streamablehttp":  # pragma: no branch
                     assert isinstance(server_params_instance, StreamableHttpParameters)
-                    mock_specific_client_func.assert_called_once_with(
-                        url=server_params_instance.url,
-                        headers=server_params_instance.headers,
-                        timeout=server_params_instance.timeout,
-                        sse_read_timeout=server_params_instance.sse_read_timeout,
-                        terminate_on_close=server_params_instance.terminate_on_close,
-                    )
+                    # Verify streamable_http_client was called with url, httpx_client, and terminate_on_close
+                    # The http_client is created by the real create_mcp_http_client
+                    import httpx
+
+                    call_args = mock_specific_client_func.call_args
+                    assert call_args.kwargs["url"] == server_params_instance.url
+                    assert call_args.kwargs["terminate_on_close"] == server_params_instance.terminate_on_close
+                    assert isinstance(call_args.kwargs["http_client"], httpx.AsyncClient)
 
                 mock_client_cm_instance.__aenter__.assert_awaited_once()
 
diff --git a/tests/server/fastmcp/test_integration.py b/tests/server/fastmcp/test_integration.py
index b1cefca29..70948bd7e 100644
--- a/tests/server/fastmcp/test_integration.py
+++ b/tests/server/fastmcp/test_integration.py
@@ -34,7 +34,7 @@
 )
 from mcp.client.session import ClientSession
 from mcp.client.sse import sse_client
-from mcp.client.streamable_http import GetSessionIdCallback, streamablehttp_client
+from mcp.client.streamable_http import GetSessionIdCallback, streamable_http_client
 from mcp.shared.context import RequestContext
 from mcp.shared.message import SessionMessage
 from mcp.shared.session import RequestResponder
@@ -179,7 +179,7 @@ def create_client_for_transport(transport: str, server_url: str):
         return sse_client(endpoint)
     elif transport == "streamable-http":
         endpoint = f"{server_url}/mcp"
-        return streamablehttp_client(endpoint)
+        return streamable_http_client(endpoint)
     else:  # pragma: no cover
         raise ValueError(f"Invalid transport: {transport}")
 
diff --git a/tests/shared/test_streamable_http.py b/tests/shared/test_streamable_http.py
index a626e7385..731dd20dd 100644
--- a/tests/shared/test_streamable_http.py
+++ b/tests/shared/test_streamable_http.py
@@ -9,6 +9,7 @@
 import socket
 import time
 from collections.abc import Generator
+from datetime import timedelta
 from typing import Any
 from unittest.mock import MagicMock
 
@@ -25,7 +26,11 @@
 
 import mcp.types as types
 from mcp.client.session import ClientSession
-from mcp.client.streamable_http import StreamableHTTPTransport, streamablehttp_client
+from mcp.client.streamable_http import (
+    StreamableHTTPTransport,
+    streamable_http_client,
+    streamablehttp_client,  # pyright: ignore[reportDeprecated]
+)
 from mcp.server import Server
 from mcp.server.streamable_http import (
     MCP_PROTOCOL_VERSION_HEADER,
@@ -40,6 +45,7 @@
 )
 from mcp.server.streamable_http_manager import StreamableHTTPSessionManager
 from mcp.server.transport_security import TransportSecuritySettings
+from mcp.shared._httpx_utils import create_mcp_http_client
 from mcp.shared.context import RequestContext
 from mcp.shared.exceptions import McpError
 from mcp.shared.message import ClientMessageMetadata, ServerMessageMetadata, SessionMessage
@@ -972,7 +978,7 @@ async def http_client(basic_server: None, basic_server_url: str):  # pragma: no
 @pytest.fixture
 async def initialized_client_session(basic_server: None, basic_server_url: str):
     """Create initialized StreamableHTTP client session."""
-    async with streamablehttp_client(f"{basic_server_url}/mcp") as (
+    async with streamable_http_client(f"{basic_server_url}/mcp") as (
         read_stream,
         write_stream,
         _,
@@ -986,9 +992,9 @@ async def initialized_client_session(basic_server: None, basic_server_url: str):
 
 
 @pytest.mark.anyio
-async def test_streamablehttp_client_basic_connection(basic_server: None, basic_server_url: str):
+async def test_streamable_http_client_basic_connection(basic_server: None, basic_server_url: str):
     """Test basic client connection with initialization."""
-    async with streamablehttp_client(f"{basic_server_url}/mcp") as (
+    async with streamable_http_client(f"{basic_server_url}/mcp") as (
         read_stream,
         write_stream,
         _,
@@ -1004,7 +1010,7 @@ async def test_streamablehttp_client_basic_connection(basic_server: None, basic_
 
 
 @pytest.mark.anyio
-async def test_streamablehttp_client_resource_read(initialized_client_session: ClientSession):
+async def test_streamable_http_client_resource_read(initialized_client_session: ClientSession):
     """Test client resource read functionality."""
     response = await initialized_client_session.read_resource(uri=AnyUrl("foobar://test-resource"))
     assert len(response.contents) == 1
@@ -1014,7 +1020,7 @@ async def test_streamablehttp_client_resource_read(initialized_client_session: C
 
 
 @pytest.mark.anyio
-async def test_streamablehttp_client_tool_invocation(initialized_client_session: ClientSession):
+async def test_streamable_http_client_tool_invocation(initialized_client_session: ClientSession):
     """Test client tool invocation."""
     # First list tools
     tools = await initialized_client_session.list_tools()
@@ -1029,7 +1035,7 @@ async def test_streamablehttp_client_tool_invocation(initialized_client_session:
 
 
 @pytest.mark.anyio
-async def test_streamablehttp_client_error_handling(initialized_client_session: ClientSession):
+async def test_streamable_http_client_error_handling(initialized_client_session: ClientSession):
     """Test error handling in client."""
     with pytest.raises(McpError) as exc_info:
         await initialized_client_session.read_resource(uri=AnyUrl("unknown://test-error"))
@@ -1038,9 +1044,9 @@ async def test_streamablehttp_client_error_handling(initialized_client_session:
 
 
 @pytest.mark.anyio
-async def test_streamablehttp_client_session_persistence(basic_server: None, basic_server_url: str):
+async def test_streamable_http_client_session_persistence(basic_server: None, basic_server_url: str):
     """Test that session ID persists across requests."""
-    async with streamablehttp_client(f"{basic_server_url}/mcp") as (
+    async with streamable_http_client(f"{basic_server_url}/mcp") as (
         read_stream,
         write_stream,
         _,
@@ -1066,9 +1072,9 @@ async def test_streamablehttp_client_session_persistence(basic_server: None, bas
 
 
 @pytest.mark.anyio
-async def test_streamablehttp_client_json_response(json_response_server: None, json_server_url: str):
+async def test_streamable_http_client_json_response(json_response_server: None, json_server_url: str):
     """Test client with JSON response mode."""
-    async with streamablehttp_client(f"{json_server_url}/mcp") as (
+    async with streamable_http_client(f"{json_server_url}/mcp") as (
         read_stream,
         write_stream,
         _,
@@ -1094,7 +1100,7 @@ async def test_streamablehttp_client_json_response(json_response_server: None, j
 
 
 @pytest.mark.anyio
-async def test_streamablehttp_client_get_stream(basic_server: None, basic_server_url: str):
+async def test_streamable_http_client_get_stream(basic_server: None, basic_server_url: str):
     """Test GET stream functionality for server-initiated messages."""
     import mcp.types as types
 
@@ -1107,7 +1113,7 @@ async def message_handler(  # pragma: no branch
         if isinstance(message, types.ServerNotification):  # pragma: no branch
             notifications_received.append(message)
 
-    async with streamablehttp_client(f"{basic_server_url}/mcp") as (
+    async with streamable_http_client(f"{basic_server_url}/mcp") as (
         read_stream,
         write_stream,
         _,
@@ -1134,13 +1140,13 @@ async def message_handler(  # pragma: no branch
 
 
 @pytest.mark.anyio
-async def test_streamablehttp_client_session_termination(basic_server: None, basic_server_url: str):
+async def test_streamable_http_client_session_termination(basic_server: None, basic_server_url: str):
     """Test client session termination functionality."""
 
     captured_session_id = None
 
-    # Create the streamablehttp_client with a custom httpx client to capture headers
-    async with streamablehttp_client(f"{basic_server_url}/mcp") as (
+    # Create the streamable_http_client with a custom httpx client to capture headers
+    async with streamable_http_client(f"{basic_server_url}/mcp") as (
         read_stream,
         write_stream,
         get_session_id,
@@ -1160,22 +1166,23 @@ async def test_streamablehttp_client_session_termination(basic_server: None, bas
     if captured_session_id:  # pragma: no cover
         headers[MCP_SESSION_ID_HEADER] = captured_session_id
 
-    async with streamablehttp_client(f"{basic_server_url}/mcp", headers=headers) as (
-        read_stream,
-        write_stream,
-        _,
-    ):
-        async with ClientSession(read_stream, write_stream) as session:
-            # Attempt to make a request after termination
-            with pytest.raises(  # pragma: no branch
-                McpError,
-                match="Session terminated",
-            ):
-                await session.list_tools()
+    async with create_mcp_http_client(headers=headers) as httpx_client:
+        async with streamable_http_client(f"{basic_server_url}/mcp", http_client=httpx_client) as (
+            read_stream,
+            write_stream,
+            _,
+        ):
+            async with ClientSession(read_stream, write_stream) as session:  # pragma: no branch
+                # Attempt to make a request after termination
+                with pytest.raises(  # pragma: no branch
+                    McpError,
+                    match="Session terminated",
+                ):
+                    await session.list_tools()
 
 
 @pytest.mark.anyio
-async def test_streamablehttp_client_session_termination_204(
+async def test_streamable_http_client_session_termination_204(
     basic_server: None, basic_server_url: str, monkeypatch: pytest.MonkeyPatch
 ):
     """Test client session termination functionality with a 204 response.
@@ -1205,8 +1212,8 @@ async def mock_delete(self: httpx.AsyncClient, *args: Any, **kwargs: Any) -> htt
 
     captured_session_id = None
 
-    # Create the streamablehttp_client with a custom httpx client to capture headers
-    async with streamablehttp_client(f"{basic_server_url}/mcp") as (
+    # Create the streamable_http_client with a custom httpx client to capture headers
+    async with streamable_http_client(f"{basic_server_url}/mcp") as (
         read_stream,
         write_stream,
         get_session_id,
@@ -1226,22 +1233,23 @@ async def mock_delete(self: httpx.AsyncClient, *args: Any, **kwargs: Any) -> htt
     if captured_session_id:  # pragma: no cover
         headers[MCP_SESSION_ID_HEADER] = captured_session_id
 
-    async with streamablehttp_client(f"{basic_server_url}/mcp", headers=headers) as (
-        read_stream,
-        write_stream,
-        _,
-    ):
-        async with ClientSession(read_stream, write_stream) as session:
-            # Attempt to make a request after termination
-            with pytest.raises(  # pragma: no branch
-                McpError,
-                match="Session terminated",
-            ):
-                await session.list_tools()
+    async with create_mcp_http_client(headers=headers) as httpx_client:
+        async with streamable_http_client(f"{basic_server_url}/mcp", http_client=httpx_client) as (
+            read_stream,
+            write_stream,
+            _,
+        ):
+            async with ClientSession(read_stream, write_stream) as session:  # pragma: no branch
+                # Attempt to make a request after termination
+                with pytest.raises(  # pragma: no branch
+                    McpError,
+                    match="Session terminated",
+                ):
+                    await session.list_tools()
 
 
 @pytest.mark.anyio
-async def test_streamablehttp_client_resumption(event_server: tuple[SimpleEventStore, str]):
+async def test_streamable_http_client_resumption(event_server: tuple[SimpleEventStore, str]):
     """Test client session resumption using sync primitives for reliable coordination."""
     _, server_url = event_server
 
@@ -1268,7 +1276,7 @@ async def on_resumption_token_update(token: str) -> None:
         captured_resumption_token = token
 
     # First, start the client session and begin the tool that waits on lock
-    async with streamablehttp_client(f"{server_url}/mcp", terminate_on_close=False) as (
+    async with streamable_http_client(f"{server_url}/mcp", terminate_on_close=False) as (
         read_stream,
         write_stream,
         get_session_id,
@@ -1324,42 +1332,44 @@ async def run_tool():
         headers[MCP_SESSION_ID_HEADER] = captured_session_id
     if captured_protocol_version:  # pragma: no cover
         headers[MCP_PROTOCOL_VERSION_HEADER] = captured_protocol_version
-    async with streamablehttp_client(f"{server_url}/mcp", headers=headers) as (
-        read_stream,
-        write_stream,
-        _,
-    ):
-        async with ClientSession(read_stream, write_stream, message_handler=message_handler) as session:
-            result = await session.send_request(
-                types.ClientRequest(
-                    types.CallToolRequest(
-                        params=types.CallToolRequestParams(name="release_lock", arguments={}),
-                    )
-                ),
-                types.CallToolResult,
-            )
-            metadata = ClientMessageMetadata(
-                resumption_token=captured_resumption_token,
-            )
 
-            result = await session.send_request(
-                types.ClientRequest(
-                    types.CallToolRequest(
-                        params=types.CallToolRequestParams(name="wait_for_lock_with_notification", arguments={}),
-                    )
-                ),
-                types.CallToolResult,
-                metadata=metadata,
-            )
-            assert len(result.content) == 1
-            assert result.content[0].type == "text"
-            assert result.content[0].text == "Completed"
+    async with create_mcp_http_client(headers=headers) as httpx_client:
+        async with streamable_http_client(f"{server_url}/mcp", http_client=httpx_client) as (
+            read_stream,
+            write_stream,
+            _,
+        ):
+            async with ClientSession(read_stream, write_stream, message_handler=message_handler) as session:
+                result = await session.send_request(
+                    types.ClientRequest(
+                        types.CallToolRequest(
+                            params=types.CallToolRequestParams(name="release_lock", arguments={}),
+                        )
+                    ),
+                    types.CallToolResult,
+                )
+                metadata = ClientMessageMetadata(
+                    resumption_token=captured_resumption_token,
+                )
 
-            # We should have received the remaining notifications
-            assert len(captured_notifications) == 1
+                result = await session.send_request(
+                    types.ClientRequest(
+                        types.CallToolRequest(
+                            params=types.CallToolRequestParams(name="wait_for_lock_with_notification", arguments={}),
+                        )
+                    ),
+                    types.CallToolResult,
+                    metadata=metadata,
+                )
+                assert len(result.content) == 1
+                assert result.content[0].type == "text"
+                assert result.content[0].text == "Completed"
+
+                # We should have received the remaining notifications
+                assert len(captured_notifications) == 1
 
-            assert isinstance(captured_notifications[0].root, types.LoggingMessageNotification)
-            assert captured_notifications[0].root.params.data == "Second notification after lock"
+            assert isinstance(captured_notifications[0].root, types.LoggingMessageNotification)  # pragma: no cover
+            assert captured_notifications[0].root.params.data == "Second notification after lock"  # pragma: no cover
 
 
 @pytest.mark.anyio
@@ -1391,7 +1401,7 @@ async def sampling_callback(
         )
 
     # Create client with sampling callback
-    async with streamablehttp_client(f"{basic_server_url}/mcp") as (
+    async with streamable_http_client(f"{basic_server_url}/mcp") as (
         read_stream,
         write_stream,
         _,
@@ -1536,28 +1546,29 @@ async def test_streamablehttp_request_context_propagation(context_aware_server:
         "X-Trace-Id": "trace-123",
     }
 
-    async with streamablehttp_client(f"{basic_server_url}/mcp", headers=custom_headers) as (
-        read_stream,
-        write_stream,
-        _,
-    ):
-        async with ClientSession(read_stream, write_stream) as session:
-            result = await session.initialize()
-            assert isinstance(result, InitializeResult)
-            assert result.serverInfo.name == "ContextAwareServer"
+    async with create_mcp_http_client(headers=custom_headers) as httpx_client:
+        async with streamable_http_client(f"{basic_server_url}/mcp", http_client=httpx_client) as (
+            read_stream,
+            write_stream,
+            _,
+        ):
+            async with ClientSession(read_stream, write_stream) as session:  # pragma: no branch
+                result = await session.initialize()
+                assert isinstance(result, InitializeResult)
+                assert result.serverInfo.name == "ContextAwareServer"
 
-            # Call the tool that echoes headers back
-            tool_result = await session.call_tool("echo_headers", {})
+                # Call the tool that echoes headers back
+                tool_result = await session.call_tool("echo_headers", {})
 
-            # Parse the JSON response
-            assert len(tool_result.content) == 1
-            assert isinstance(tool_result.content[0], TextContent)
-            headers_data = json.loads(tool_result.content[0].text)
+                # Parse the JSON response
+                assert len(tool_result.content) == 1
+                assert isinstance(tool_result.content[0], TextContent)
+                headers_data = json.loads(tool_result.content[0].text)
 
-            # Verify headers were propagated
-            assert headers_data.get("authorization") == "Bearer test-token"
-            assert headers_data.get("x-custom-header") == "test-value"
-            assert headers_data.get("x-trace-id") == "trace-123"
+                # Verify headers were propagated
+                assert headers_data.get("authorization") == "Bearer test-token"
+                assert headers_data.get("x-custom-header") == "test-value"
+                assert headers_data.get("x-trace-id") == "trace-123"
 
 
 @pytest.mark.anyio
@@ -1573,17 +1584,22 @@ async def test_streamablehttp_request_context_isolation(context_aware_server: No
             "Authorization": f"Bearer token-{i}",
         }
 
-        async with streamablehttp_client(f"{basic_server_url}/mcp", headers=headers) as (read_stream, write_stream, _):
-            async with ClientSession(read_stream, write_stream) as session:
-                await session.initialize()
+        async with create_mcp_http_client(headers=headers) as httpx_client:
+            async with streamable_http_client(f"{basic_server_url}/mcp", http_client=httpx_client) as (
+                read_stream,
+                write_stream,
+                _,
+            ):
+                async with ClientSession(read_stream, write_stream) as session:  # pragma: no branch
+                    await session.initialize()
 
-                # Call the tool that echoes context
-                tool_result = await session.call_tool("echo_context", {"request_id": f"request-{i}"})
+                    # Call the tool that echoes context
+                    tool_result = await session.call_tool("echo_context", {"request_id": f"request-{i}"})
 
-                assert len(tool_result.content) == 1
-                assert isinstance(tool_result.content[0], TextContent)
-                context_data = json.loads(tool_result.content[0].text)
-                contexts.append(context_data)
+                    assert len(tool_result.content) == 1
+                    assert isinstance(tool_result.content[0], TextContent)
+                    context_data = json.loads(tool_result.content[0].text)
+                    contexts.append(context_data)
 
     # Verify each request had its own context
     assert len(contexts) == 3  # pragma: no cover
@@ -1597,7 +1613,7 @@ async def test_streamablehttp_request_context_isolation(context_aware_server: No
 @pytest.mark.anyio
 async def test_client_includes_protocol_version_header_after_init(context_aware_server: None, basic_server_url: str):
     """Test that client includes mcp-protocol-version header after initialization."""
-    async with streamablehttp_client(f"{basic_server_url}/mcp") as (
+    async with streamable_http_client(f"{basic_server_url}/mcp") as (
         read_stream,
         write_stream,
         _,
@@ -1713,7 +1729,7 @@ async def test_client_crash_handled(basic_server: None, basic_server_url: str):
     # Simulate bad client that crashes after init
     async def bad_client():
         """Client that triggers ClosedResourceError"""
-        async with streamablehttp_client(f"{basic_server_url}/mcp") as (
+        async with streamable_http_client(f"{basic_server_url}/mcp") as (
             read_stream,
             write_stream,
             _,
@@ -1731,7 +1747,7 @@ async def bad_client():
         await anyio.sleep(0.1)
 
     # Try a good client, it should still be able to connect and list tools
-    async with streamablehttp_client(f"{basic_server_url}/mcp") as (
+    async with streamable_http_client(f"{basic_server_url}/mcp") as (
         read_stream,
         write_stream,
         _,
@@ -1880,7 +1896,7 @@ async def test_close_sse_stream_callback_not_provided_for_old_protocol_version()
 
 
 @pytest.mark.anyio
-async def test_streamablehttp_client_receives_priming_event(
+async def test_streamable_http_client_receives_priming_event(
     event_server: tuple[SimpleEventStore, str],
 ) -> None:
     """Client should receive priming event (resumption token update) on POST SSE stream."""
@@ -1891,7 +1907,7 @@ async def test_streamablehttp_client_receives_priming_event(
     async def on_resumption_token_update(token: str) -> None:
         captured_resumption_tokens.append(token)
 
-    async with streamablehttp_client(f"{server_url}/mcp") as (
+    async with streamable_http_client(f"{server_url}/mcp") as (
         read_stream,
         write_stream,
         _,
@@ -1932,7 +1948,7 @@ async def test_server_close_sse_stream_via_context(
     """Server tool can call ctx.close_sse_stream() to close connection."""
     _, server_url = event_server
 
-    async with streamablehttp_client(f"{server_url}/mcp") as (
+    async with streamable_http_client(f"{server_url}/mcp") as (
         read_stream,
         write_stream,
         _,
@@ -1953,7 +1969,7 @@ async def test_server_close_sse_stream_via_context(
 
 
 @pytest.mark.anyio
-async def test_streamablehttp_client_auto_reconnects(
+async def test_streamable_http_client_auto_reconnects(
     event_server: tuple[SimpleEventStore, str],
 ) -> None:
     """Client should auto-reconnect with Last-Event-ID when server closes after priming event."""
@@ -1969,7 +1985,7 @@ async def message_handler(
             if isinstance(message.root, types.LoggingMessageNotification):  # pragma: no branch
                 captured_notifications.append(str(message.root.params.data))
 
-    async with streamablehttp_client(f"{server_url}/mcp") as (
+    async with streamable_http_client(f"{server_url}/mcp") as (
         read_stream,
         write_stream,
         _,
@@ -1998,13 +2014,13 @@ async def message_handler(
 
 
 @pytest.mark.anyio
-async def test_streamablehttp_client_respects_retry_interval(
+async def test_streamable_http_client_respects_retry_interval(
     event_server: tuple[SimpleEventStore, str],
 ) -> None:
     """Client MUST respect retry field, waiting specified ms before reconnecting."""
     _, server_url = event_server
 
-    async with streamablehttp_client(f"{server_url}/mcp") as (
+    async with streamable_http_client(f"{server_url}/mcp") as (
         read_stream,
         write_stream,
         _,
@@ -2029,7 +2045,7 @@ async def test_streamablehttp_client_respects_retry_interval(
 
 
 @pytest.mark.anyio
-async def test_streamablehttp_sse_polling_full_cycle(
+async def test_streamable_http_sse_polling_full_cycle(
     event_server: tuple[SimpleEventStore, str],
 ) -> None:
     """End-to-end test: server closes stream, client reconnects, receives all events."""
@@ -2045,7 +2061,7 @@ async def message_handler(
             if isinstance(message.root, types.LoggingMessageNotification):  # pragma: no branch
                 all_notifications.append(str(message.root.params.data))
 
-    async with streamablehttp_client(f"{server_url}/mcp") as (
+    async with streamable_http_client(f"{server_url}/mcp") as (
         read_stream,
         write_stream,
         _,
@@ -2077,7 +2093,7 @@ async def message_handler(
 
 
 @pytest.mark.anyio
-async def test_streamablehttp_events_replayed_after_disconnect(
+async def test_streamable_http_events_replayed_after_disconnect(
     event_server: tuple[SimpleEventStore, str],
 ) -> None:
     """Events sent while client is disconnected should be replayed on reconnect."""
@@ -2093,7 +2109,7 @@ async def message_handler(
             if isinstance(message.root, types.LoggingMessageNotification):  # pragma: no branch
                 notification_data.append(str(message.root.params.data))
 
-    async with streamablehttp_client(f"{server_url}/mcp") as (
+    async with streamable_http_client(f"{server_url}/mcp") as (
         read_stream,
         write_stream,
         _,
@@ -2125,7 +2141,7 @@ async def message_handler(
 
 
 @pytest.mark.anyio
-async def test_streamablehttp_multiple_reconnections(
+async def test_streamable_http_multiple_reconnections(
     event_server: tuple[SimpleEventStore, str],
 ):
     """Verify multiple close_sse_stream() calls each trigger a client reconnect.
@@ -2145,7 +2161,7 @@ async def test_streamablehttp_multiple_reconnections(
     async def on_resumption_token(token: str) -> None:
         resumption_tokens.append(token)
 
-    async with streamablehttp_client(f"{server_url}/mcp") as (read_stream, write_stream, _):
+    async with streamable_http_client(f"{server_url}/mcp") as (read_stream, write_stream, _):
         async with ClientSession(read_stream, write_stream) as session:
             await session.initialize()
 
@@ -2205,7 +2221,7 @@ async def message_handler(
             if isinstance(message.root, types.ResourceUpdatedNotification):  # pragma: no branch
                 received_notifications.append(str(message.root.params.uri))
 
-    async with streamablehttp_client(f"{server_url}/mcp") as (
+    async with streamable_http_client(f"{server_url}/mcp") as (
         read_stream,
         write_stream,
         _,
@@ -2236,3 +2252,145 @@ async def message_handler(
             assert "http://notification_2/" in received_notifications, (
                 f"Should receive notification 2 after reconnect, got: {received_notifications}"
             )
+
+
+@pytest.mark.anyio
+async def test_streamable_http_client_does_not_mutate_provided_client(
+    basic_server: None, basic_server_url: str
+) -> None:
+    """Test that streamable_http_client does not mutate the provided httpx client's headers."""
+    # Create a client with custom headers
+    original_headers = {
+        "X-Custom-Header": "custom-value",
+        "Authorization": "Bearer test-token",
+    }
+
+    async with httpx.AsyncClient(headers=original_headers, follow_redirects=True) as custom_client:
+        # Use the client with streamable_http_client
+        async with streamable_http_client(f"{basic_server_url}/mcp", http_client=custom_client) as (
+            read_stream,
+            write_stream,
+            _,
+        ):
+            async with ClientSession(read_stream, write_stream) as session:
+                result = await session.initialize()
+                assert isinstance(result, InitializeResult)
+
+        # Verify client headers were not mutated with MCP protocol headers
+        # If accept header exists, it should still be httpx default, not MCP's
+        if "accept" in custom_client.headers:  # pragma: no branch
+            assert custom_client.headers.get("accept") == "*/*"
+        # MCP content-type should not have been added
+        assert custom_client.headers.get("content-type") != "application/json"
+
+        # Verify custom headers are still present and unchanged
+        assert custom_client.headers.get("X-Custom-Header") == "custom-value"
+        assert custom_client.headers.get("Authorization") == "Bearer test-token"
+
+
+@pytest.mark.anyio
+async def test_streamable_http_client_mcp_headers_override_defaults(
+    context_aware_server: None, basic_server_url: str
+) -> None:
+    """Test that MCP protocol headers override httpx.AsyncClient default headers."""
+    # httpx.AsyncClient has default "accept: */*" header
+    # We need to verify that our MCP accept header overrides it in actual requests
+
+    async with httpx.AsyncClient(follow_redirects=True) as client:
+        # Verify client has default accept header
+        assert client.headers.get("accept") == "*/*"
+
+        async with streamable_http_client(f"{basic_server_url}/mcp", http_client=client) as (
+            read_stream,
+            write_stream,
+            _,
+        ):
+            async with ClientSession(read_stream, write_stream) as session:  # pragma: no branch
+                await session.initialize()
+
+                # Use echo_headers tool to see what headers the server actually received
+                tool_result = await session.call_tool("echo_headers", {})
+                assert len(tool_result.content) == 1
+                assert isinstance(tool_result.content[0], TextContent)
+                headers_data = json.loads(tool_result.content[0].text)
+
+                # Verify MCP protocol headers were sent (not httpx defaults)
+                assert "accept" in headers_data
+                assert "application/json" in headers_data["accept"]
+                assert "text/event-stream" in headers_data["accept"]
+
+                assert "content-type" in headers_data
+                assert headers_data["content-type"] == "application/json"
+
+
+@pytest.mark.anyio
+async def test_streamable_http_client_preserves_custom_with_mcp_headers(
+    context_aware_server: None, basic_server_url: str
+) -> None:
+    """Test that both custom headers and MCP protocol headers are sent in requests."""
+    custom_headers = {
+        "X-Custom-Header": "custom-value",
+        "X-Request-Id": "req-123",
+        "Authorization": "Bearer test-token",
+    }
+
+    async with httpx.AsyncClient(headers=custom_headers, follow_redirects=True) as client:
+        async with streamable_http_client(f"{basic_server_url}/mcp", http_client=client) as (
+            read_stream,
+            write_stream,
+            _,
+        ):
+            async with ClientSession(read_stream, write_stream) as session:  # pragma: no branch
+                await session.initialize()
+
+                # Use echo_headers tool to verify both custom and MCP headers are present
+                tool_result = await session.call_tool("echo_headers", {})
+                assert len(tool_result.content) == 1
+                assert isinstance(tool_result.content[0], TextContent)
+                headers_data = json.loads(tool_result.content[0].text)
+
+                # Verify custom headers are present
+                assert headers_data.get("x-custom-header") == "custom-value"
+                assert headers_data.get("x-request-id") == "req-123"
+                assert headers_data.get("authorization") == "Bearer test-token"
+
+                # Verify MCP protocol headers are also present
+                assert "accept" in headers_data
+                assert "application/json" in headers_data["accept"]
+                assert "text/event-stream" in headers_data["accept"]
+
+                assert "content-type" in headers_data
+                assert headers_data["content-type"] == "application/json"
+
+
+@pytest.mark.anyio
+async def test_streamable_http_transport_deprecated_params_ignored(basic_server: None, basic_server_url: str) -> None:
+    """Test that deprecated parameters passed to StreamableHTTPTransport are properly ignored."""
+    with pytest.warns(DeprecationWarning):
+        transport = StreamableHTTPTransport(  # pyright: ignore[reportDeprecated]
+            url=f"{basic_server_url}/mcp",
+            headers={"X-Should-Be-Ignored": "ignored"},
+            timeout=999,
+            sse_read_timeout=timedelta(seconds=999),
+            auth=None,
+        )
+
+    headers = transport._prepare_headers()
+    assert "X-Should-Be-Ignored" not in headers
+    assert headers["accept"] == "application/json, text/event-stream"
+    assert headers["content-type"] == "application/json"
+
+
+@pytest.mark.anyio
+async def test_streamablehttp_client_deprecation_warning(basic_server: None, basic_server_url: str) -> None:
+    """Test that the old streamablehttp_client() function issues a deprecation warning."""
+    with pytest.warns(DeprecationWarning, match="Use `streamable_http_client` instead"):
+        async with streamablehttp_client(f"{basic_server_url}/mcp") as (  # pyright: ignore[reportDeprecated]
+            read_stream,
+            write_stream,
+            _,
+        ):
+            async with ClientSession(read_stream, write_stream) as session:  # pragma: no branch
+                await session.initialize()
+                tools = await session.list_tools()
+                assert len(tools.tools) > 0