diff --git a/scripts/seed.py b/scripts/seed.py
index f3fbfa8..24d4843 100644
--- a/scripts/seed.py
+++ b/scripts/seed.py
@@ -206,14 +206,13 @@ def seed_model(model_version, session, lite: bool = False) -> TaxBenefitModelVer
                 f"  [green]✓[/green] Added {len(model_version.variables)} variables"
             )
 
-        # Add parameters (only user-facing ones: those with labels)
-        # Deduplicate by name - keep first occurrence
+        # Add parameters - deduplicate by name (keep first occurrence)
         # In lite mode, exclude US state parameters (gov.states.*)
         seen_names = set()
         parameters_to_add = []
         skipped_state_params = 0
         for p in model_version.parameters:
-            if p.label is None or p.name in seen_names:
+            if p.name in seen_names:
                 continue
             # In lite mode, skip state-level parameters for faster seeding
             if lite and p.name.startswith("gov.states."):
@@ -222,8 +221,10 @@ def seed_model(model_version, session, lite: bool = False) -> TaxBenefitModelVer
             parameters_to_add.append(p)
             seen_names.add(p.name)
 
-        filter_msg = f"  Filtered to {len(parameters_to_add)} user-facing parameters"
-        filter_msg += f" (from {len(model_version.parameters)} total, deduplicated by name)"
+        filter_msg = f"  Filtered to {len(parameters_to_add)} parameters"
+        filter_msg += (
+            f" (from {len(model_version.parameters)} total, deduplicated by name)"
+        )
         if lite and skipped_state_params > 0:
             filter_msg += f", skipped {skipped_state_params} state params (lite mode)"
         console.print(filter_msg)
@@ -626,7 +627,9 @@ def main():
 
     with logfire.span("database_seeding"):
         mode_str = " (lite mode)" if args.lite else ""
-        console.print(f"[bold green]PolicyEngine database seeding{mode_str}[/bold green]\n")
+        console.print(
+            f"[bold green]PolicyEngine database seeding{mode_str}[/bold green]\n"
+        )
 
         with next(get_quiet_session()) as session:
             # Seed UK model
diff --git a/src/policyengine_api/agent_sandbox.py b/src/policyengine_api/agent_sandbox.py
index 57f7faf..604125a 100644
--- a/src/policyengine_api/agent_sandbox.py
+++ b/src/policyengine_api/agent_sandbox.py
@@ -235,8 +235,7 @@ def openapi_to_claude_tools(spec: dict) -> list[dict]:
 
                 prop = schema_to_json_schema(spec, param_schema)
                 prop["description"] = (
-                    param.get("description", "")
-                    + f" (in: {param_in})"
+                    param.get("description", "") + f" (in: {param_in})"
                 )
                 properties[param_name] = prop
 
@@ -268,16 +267,18 @@ def openapi_to_claude_tools(spec: dict) -> list[dict]:
             if required:
                 input_schema["required"] = list(set(required))
 
-            tools.append({
-                "name": tool_name,
-                "description": full_desc[:1024],  # Claude has limits
-                "input_schema": input_schema,
-                "_meta": {
-                    "path": path,
-                    "method": method,
-                    "parameters": operation.get("parameters", []),
-                },
-            })
+            tools.append(
+                {
+                    "name": tool_name,
+                    "description": full_desc[:1024],  # Claude has limits
+                    "input_schema": input_schema,
+                    "_meta": {
+                        "path": path,
+                        "method": method,
+                        "parameters": operation.get("parameters", []),
+                    },
+                }
+            )
 
     return tools
 
@@ -347,7 +348,9 @@ def execute_api_tool(
                 url, params=query_params, json=body_data, headers=headers, timeout=60
             )
         elif method == "delete":
-            resp = requests.delete(url, params=query_params, headers=headers, timeout=60)
+            resp = requests.delete(
+                url, params=query_params, headers=headers, timeout=60
+            )
         else:
             return f"Unsupported method: {method}"
 
@@ -415,9 +418,7 @@ def log(msg: str) -> None:
     tool_lookup = {t["name"]: t for t in tools}
 
     # Strip _meta from tools before sending to Claude (it doesn't need it)
-    claude_tools = [
-        {k: v for k, v in t.items() if k != "_meta"} for t in tools
-    ]
+    claude_tools = [{k: v for k, v in t.items() if k != "_meta"} for t in tools]
     # Add the sleep tool
     claude_tools.append(SLEEP_TOOL)
 
@@ -477,11 +478,13 @@ def log(msg: str) -> None:
 
                 log(f"[TOOL_RESULT] {result[:300]}")
 
-                tool_results.append({
-                    "type": "tool_result",
-                    "tool_use_id": block.id,
-                    "content": result,
-                })
+                tool_results.append(
+                    {
+                        "type": "tool_result",
+                        "tool_use_id": block.id,
+                        "content": result,
+                    }
+                )
 
         messages.append({"role": "assistant", "content": assistant_content})
 
diff --git a/src/policyengine_api/api/agent.py b/src/policyengine_api/api/agent.py
index 7b7d108..6c26e80 100644
--- a/src/policyengine_api/api/agent.py
+++ b/src/policyengine_api/api/agent.py
@@ -24,6 +24,7 @@ def get_traceparent() -> str | None:
     TraceContextTextMapPropagator().inject(carrier)
     return carrier.get("traceparent")
 
+
 router = APIRouter(prefix="/agent", tags=["agent"])
 
 
@@ -93,7 +94,9 @@ def _run_local_agent(
     from policyengine_api.agent_sandbox import _run_agent_impl
 
     try:
-        history_dicts = [{"role": m.role, "content": m.content} for m in (history or [])]
+        history_dicts = [
+            {"role": m.role, "content": m.content} for m in (history or [])
+        ]
         result = _run_agent_impl(question, api_base_url, call_id, history_dicts)
         _calls[call_id]["status"] = result.get("status", "completed")
         _calls[call_id]["result"] = result
@@ -136,9 +139,15 @@ async def run_agent(request: RunRequest) -> RunResponse:
 
         traceparent = get_traceparent()
         run_fn = modal.Function.from_name("policyengine-sandbox", "run_agent")
-        history_dicts = [{"role": m.role, "content": m.content} for m in request.history]
+        history_dicts = [
+            {"role": m.role, "content": m.content} for m in request.history
+        ]
         call = run_fn.spawn(
-            request.question, api_base_url, call_id, history_dicts, traceparent=traceparent
+            request.question,
+            api_base_url,
+            call_id,
+            history_dicts,
+            traceparent=traceparent,
         )
 
         _calls[call_id] = {
@@ -166,7 +175,12 @@ async def run_agent(request: RunRequest) -> RunResponse:
         # Run in background using asyncio
         loop = asyncio.get_event_loop()
         loop.run_in_executor(
-            None, _run_local_agent, call_id, request.question, api_base_url, request.history
+            None,
+            _run_local_agent,
+            call_id,
+            request.question,
+            api_base_url,
+            request.history,
         )
 
     return RunResponse(call_id=call_id, status="running")
diff --git a/src/policyengine_api/api/household.py b/src/policyengine_api/api/household.py
index b0e99c9..09ea701 100644
--- a/src/policyengine_api/api/household.py
+++ b/src/policyengine_api/api/household.py
@@ -28,6 +28,7 @@ def get_traceparent() -> str | None:
     TraceContextTextMapPropagator().inject(carrier)
     return carrier.get("traceparent")
 
+
 router = APIRouter(prefix="/household", tags=["household"])
 
 
diff --git a/src/policyengine_api/api/variables.py b/src/policyengine_api/api/variables.py
index d660b1b..3c24f3d 100644
--- a/src/policyengine_api/api/variables.py
+++ b/src/policyengine_api/api/variables.py
@@ -56,9 +56,9 @@ def list_variables(
         # Case-insensitive search using ILIKE
         # Note: Variables don't have a label field, only name and description
         search_pattern = f"%{search}%"
-        search_filter = Variable.name.ilike(search_pattern) | Variable.description.ilike(
+        search_filter = Variable.name.ilike(
             search_pattern
-        )
+        ) | Variable.description.ilike(search_pattern)
         query = query.where(search_filter)
 
     variables = session.exec(
diff --git a/src/policyengine_api/modal_app.py b/src/policyengine_api/modal_app.py
index cdc3d8d..3a7b9a7 100644
--- a/src/policyengine_api/modal_app.py
+++ b/src/policyengine_api/modal_app.py
@@ -147,7 +147,11 @@ def download_dataset(
 
 
 @app.function(
-    image=uk_image, secrets=[db_secrets, logfire_secrets], memory=4096, cpu=4, timeout=600
+    image=uk_image,
+    secrets=[db_secrets, logfire_secrets],
+    memory=4096,
+    cpu=4,
+    timeout=600,
 )
 def simulate_household_uk(
     job_id: str,
@@ -277,7 +281,11 @@ def simulate_household_uk(
 
 
 @app.function(
-    image=us_image, secrets=[db_secrets, logfire_secrets], memory=4096, cpu=4, timeout=600
+    image=us_image,
+    secrets=[db_secrets, logfire_secrets],
+    memory=4096,
+    cpu=4,
+    timeout=600,
 )
 def simulate_household_us(
     job_id: str,
@@ -416,7 +424,11 @@ def simulate_household_us(
 
 
 @app.function(
-    image=uk_image, secrets=[db_secrets, logfire_secrets], memory=8192, cpu=8, timeout=1800
+    image=uk_image,
+    secrets=[db_secrets, logfire_secrets],
+    memory=8192,
+    cpu=8,
+    timeout=1800,
 )
 def simulate_economy_uk(simulation_id: str, traceparent: str | None = None) -> None:
     """Run a single UK economy simulation and write results to database."""
@@ -445,6 +457,7 @@ def simulate_economy_uk(simulation_id: str, traceparent: str | None = None) -> N
                 Simulation,
                 SimulationStatus,
             )
+
             with Session(engine) as session:
                 simulation = session.get(Simulation, UUID(simulation_id))
                 if not simulation:
@@ -452,7 +465,9 @@ def simulate_economy_uk(simulation_id: str, traceparent: str | None = None) -> N
 
                 # Skip if already completed
                 if simulation.status == SimulationStatus.COMPLETED:
-                    logfire.info("Simulation already completed", simulation_id=simulation_id)
+                    logfire.info(
+                        "Simulation already completed", simulation_id=simulation_id
+                    )
                     return
 
                 # Update status to running
@@ -475,7 +490,9 @@ def simulate_economy_uk(simulation_id: str, traceparent: str | None = None) -> N
                 pe_model_version = uk_latest
 
                 # Get policy and dynamic
-                policy = _get_pe_policy_uk(simulation.policy_id, pe_model_version, session)
+                policy = _get_pe_policy_uk(
+                    simulation.policy_id, pe_model_version, session
+                )
                 dynamic = _get_pe_dynamic_uk(
                     simulation.dynamic_id, pe_model_version, session
                 )
@@ -512,7 +529,11 @@ def simulate_economy_uk(simulation_id: str, traceparent: str | None = None) -> N
             logfire.info("UK economy simulation completed", simulation_id=simulation_id)
 
         except Exception as e:
-            logfire.error("UK economy simulation failed", simulation_id=simulation_id, error=str(e))
+            logfire.error(
+                "UK economy simulation failed",
+                simulation_id=simulation_id,
+                error=str(e),
+            )
             # Use raw SQL to mark as failed - models may not be available
             try:
                 from sqlmodel import text
@@ -534,7 +555,11 @@ def simulate_economy_uk(simulation_id: str, traceparent: str | None = None) -> N
 
 
 @app.function(
-    image=us_image, secrets=[db_secrets, logfire_secrets], memory=8192, cpu=8, timeout=1800
+    image=us_image,
+    secrets=[db_secrets, logfire_secrets],
+    memory=8192,
+    cpu=8,
+    timeout=1800,
 )
 def simulate_economy_us(simulation_id: str, traceparent: str | None = None) -> None:
     """Run a single US economy simulation and write results to database."""
@@ -563,6 +588,7 @@ def simulate_economy_us(simulation_id: str, traceparent: str | None = None) -> N
                 Simulation,
                 SimulationStatus,
             )
+
             with Session(engine) as session:
                 simulation = session.get(Simulation, UUID(simulation_id))
                 if not simulation:
@@ -570,7 +596,9 @@ def simulate_economy_us(simulation_id: str, traceparent: str | None = None) -> N
 
                 # Skip if already completed
                 if simulation.status == SimulationStatus.COMPLETED:
-                    logfire.info("Simulation already completed", simulation_id=simulation_id)
+                    logfire.info(
+                        "Simulation already completed", simulation_id=simulation_id
+                    )
                     return
 
                 # Update status to running
@@ -593,7 +621,9 @@ def simulate_economy_us(simulation_id: str, traceparent: str | None = None) -> N
                 pe_model_version = us_latest
 
                 # Get policy and dynamic
-                policy = _get_pe_policy_us(simulation.policy_id, pe_model_version, session)
+                policy = _get_pe_policy_us(
+                    simulation.policy_id, pe_model_version, session
+                )
                 dynamic = _get_pe_dynamic_us(
                     simulation.dynamic_id, pe_model_version, session
                 )
@@ -630,7 +660,11 @@ def simulate_economy_us(simulation_id: str, traceparent: str | None = None) -> N
             logfire.info("US economy simulation completed", simulation_id=simulation_id)
 
         except Exception as e:
-            logfire.error("US economy simulation failed", simulation_id=simulation_id, error=str(e))
+            logfire.error(
+                "US economy simulation failed",
+                simulation_id=simulation_id,
+                error=str(e),
+            )
             # Use raw SQL to mark as failed - models may not be available
             try:
                 from sqlmodel import text
@@ -652,7 +686,11 @@ def simulate_economy_us(simulation_id: str, traceparent: str | None = None) -> N
 
 
 @app.function(
-    image=uk_image, secrets=[db_secrets, logfire_secrets], memory=8192, cpu=8, timeout=1800
+    image=uk_image,
+    secrets=[db_secrets, logfire_secrets],
+    memory=8192,
+    cpu=8,
+    timeout=1800,
 )
 def economy_comparison_uk(job_id: str, traceparent: str | None = None) -> None:
     """Run UK economy comparison analysis (decile impacts, budget impact, etc)."""
@@ -690,6 +728,7 @@ def economy_comparison_uk(job_id: str, traceparent: str | None = None) -> None:
                 SimulationStatus,
                 TaxBenefitModelVersion,
             )
+
             with Session(engine) as session:
                 # Load report and related data
                 report = session.get(Report, UUID(job_id))
@@ -851,7 +890,10 @@ def economy_comparison_uk(job_id: str, traceparent: str | None = None) -> None:
                             )
                             session.add(program_stat)
                         except KeyError as e:
-                            logfire.warn(f"Skipping {prog_name}: variable not found", error=str(e))
+                            logfire.warn(
+                                f"Skipping {prog_name}: variable not found",
+                                error=str(e),
+                            )
 
                 # Mark simulations and report as completed
                 baseline_sim.status = SimulationStatus.COMPLETED
@@ -890,7 +932,11 @@ def economy_comparison_uk(job_id: str, traceparent: str | None = None) -> None:
 
 
 @app.function(
-    image=us_image, secrets=[db_secrets, logfire_secrets], memory=8192, cpu=8, timeout=1800
+    image=us_image,
+    secrets=[db_secrets, logfire_secrets],
+    memory=8192,
+    cpu=8,
+    timeout=1800,
 )
 def economy_comparison_us(job_id: str, traceparent: str | None = None) -> None:
     """Run US economy comparison analysis (decile impacts, budget impact, etc)."""
@@ -1036,7 +1082,9 @@ def economy_comparison_us(job_id: str, traceparent: str | None = None) -> None:
 
                 # Calculate program statistics
                 with logfire.span("calculate_program_statistics"):
-                    PEProgramStats.model_rebuild(_types_namespace={"Simulation": PESimulation})
+                    PEProgramStats.model_rebuild(
+                        _types_namespace={"Simulation": PESimulation}
+                    )
 
                     programs = {
                         "income_tax": {"entity": "tax_unit", "is_tax": True},
@@ -1074,7 +1122,10 @@ def economy_comparison_us(job_id: str, traceparent: str | None = None) -> None:
                             )
                             session.add(program_stat)
                         except KeyError as e:
-                            logfire.warn(f"Skipping {prog_name}: variable not found", error=str(e))
+                            logfire.warn(
+                                f"Skipping {prog_name}: variable not found",
+                                error=str(e),
+                            )
 
                 # Mark simulations and report as completed
                 baseline_sim.status = SimulationStatus.COMPLETED
diff --git a/test_fixtures/fixtures_parameters.py b/test_fixtures/fixtures_parameters.py
index ff69b0e..12995b3 100644
--- a/test_fixtures/fixtures_parameters.py
+++ b/test_fixtures/fixtures_parameters.py
@@ -41,8 +41,17 @@ def model_version(session):
 # -----------------------------------------------------------------------------
 
 
-def create_parameter(session, model_version, name: str, label: str) -> Parameter:
-    """Create and persist a Parameter."""
+def create_parameter(
+    session, model_version, name: str, label: str | None = None
+) -> Parameter:
+    """Create and persist a Parameter.
+
+    Args:
+        session: The database session.
+        model_version: The TaxBenefitModelVersion to associate with.
+        name: The parameter name (e.g., "gov.irs.income.bracket.rates.1").
+        label: Optional human-readable label. If None, parameter has no label.
+    """
     param = Parameter(
         name=name,
         label=label,
diff --git a/tests/test_agent_policy_questions.py b/tests/test_agent_policy_questions.py
index 1550f89..68d80d0 100644
--- a/tests/test_agent_policy_questions.py
+++ b/tests/test_agent_policy_questions.py
@@ -218,4 +218,6 @@ def test_turn_efficiency(self, question, max_expected_turns):
         print(f"Result: {result['result'][:300]}")
 
         if result["turns"] > max_expected_turns:
-            print(f"WARNING: Took {result['turns']} turns, expected <= {max_expected_turns}")
+            print(
+                f"WARNING: Took {result['turns']} turns, expected <= {max_expected_turns}"
+            )
diff --git a/tests/test_parameters.py b/tests/test_parameters.py
index f95016b..72cdd8f 100644
--- a/tests/test_parameters.py
+++ b/tests/test_parameters.py
@@ -42,6 +42,60 @@ def test__given_nonexistent_parameter_id__then_returns_404(client):
     assert response.status_code == 404
 
 
+def test__given_parameter_without_label__then_can_create_and_retrieve(
+    client,
+    session,
+    model_version,  # noqa: F811
+):
+    """Parameters without labels can be created and retrieved via API.
+
+    This tests that the API supports parameters with label=None, which is
+    important for bracket parameters (e.g., [0].rate) and breakdown parameters
+    (e.g., .SINGLE, .CA) that don't have explicit labels in their YAML files.
+    """
+    # Given - create a parameter without a label (simulating bracket/breakdown params)
+    param = create_parameter(
+        session, model_version, "gov.test.rates[0].rate", label=None
+    )
+
+    # When
+    response = client.get(f"/parameters/{param.id}")
+
+    # Then
+    assert response.status_code == 200
+    data = response.json()
+    assert data["name"] == "gov.test.rates[0].rate"
+    assert data["label"] is None
+
+
+def test__given_mixed_label_parameters__then_returns_all(
+    client,
+    session,
+    model_version,  # noqa: F811
+):
+    """Parameters with and without labels are both returned in list queries.
+
+    This ensures the API doesn't filter out parameters based on label presence.
+    """
+    # Given - create parameters with and without labels
+    param_with_label = create_parameter(
+        session, model_version, "gov.test.labeled", label="Test labeled param"
+    )
+    param_without_label = create_parameter(
+        session, model_version, "gov.test.unlabeled", label=None
+    )
+
+    # When
+    response = client.get("/parameters")
+
+    # Then
+    assert response.status_code == 200
+    data = response.json()
+    param_names = [p["name"] for p in data]
+    assert param_with_label.name in param_names
+    assert param_without_label.name in param_names
+
+
 # -----------------------------------------------------------------------------
 # Parameter Value Endpoint Tests
 # -----------------------------------------------------------------------------