diff --git a/Tests/images/timeout-041dd17dfde800360a47a172269df127af138c6b.dds b/Tests/images/timeout-041dd17dfde800360a47a172269df127af138c6b.dds
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diff --git a/Tests/images/timeout-755a4d204f4208e3597ac3391edebee196462bd0.dds b/Tests/images/timeout-755a4d204f4208e3597ac3391edebee196462bd0.dds
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diff --git a/Tests/images/timeout-c60a3d7314213624607bfb3e38d551a8b24a7435.dds b/Tests/images/timeout-c60a3d7314213624607bfb3e38d551a8b24a7435.dds
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diff --git a/Tests/test_file_dds.py b/Tests/test_file_dds.py
index 931ff02f1fb..98b9e0fb586 100644
--- a/Tests/test_file_dds.py
+++ b/Tests/test_file_dds.py
@@ -15,6 +15,7 @@
     assert_image_similar,
     assert_image_similar_tofile,
     hopper,
+    timeout_unless_slower_valgrind,
 )
 
 TEST_FILE_DXT1 = "Tests/images/dxt1-rgb-4bbp-noalpha_MipMaps-1.dds"
@@ -540,3 +541,18 @@ def test_save_large_file(tmp_path: Path, pixel_format: str, mode: str) -> None:
     im = hopper(mode).resize((440, 440))
     # should not error in valgrind
     im.save(tmp_path / "img.dds", pixel_format=pixel_format)
+
+
+@timeout_unless_slower_valgrind(1)
+@pytest.mark.parametrize(
+    "test_file",
+    [
+        "Tests/images/timeout-041dd17dfde800360a47a172269df127af138c6b.dds",
+        "Tests/images/timeout-755a4d204f4208e3597ac3391edebee196462bd0.dds",
+        "Tests/images/timeout-52d106579505547091ef69b58341351a37c23e31.dds",
+        "Tests/images/timeout-c60a3d7314213624607bfb3e38d551a8b24a7435.dds",
+    ],
+)
+def test_timeout(test_file) -> None:
+    with Image.open(test_file) as im:
+        im.load()
diff --git a/src/PIL/DdsImagePlugin.py b/src/PIL/DdsImagePlugin.py
index 312f602a6b1..bfd14a2a99b 100644
--- a/src/PIL/DdsImagePlugin.py
+++ b/src/PIL/DdsImagePlugin.py
@@ -503,21 +503,34 @@ def decode(self, buffer: bytes | Image.SupportsArrayInterface) -> tuple[int, int
                 while mask >> (offset + 1) << (offset + 1) == mask:
                     offset += 1
             mask_offsets.append(offset)
-            mask_totals.append(mask >> offset)
+            mask_total = mask >> offset
+            if not mask_total:
+                mask_totals.append(0)
+            else:
+                mask_totals.append(255 / mask_total)
 
         data = bytearray()
         bytecount = bitcount // 8
         dest_length = self.state.xsize * self.state.ysize * len(masks)
-        while len(data) < dest_length:
-            value = int.from_bytes(self.fd.read(bytecount), "little")
+        # consume the data
+        has_more = True
+        while len(data) < dest_length and has_more:
+            chunk = self.fd.read(bytecount)
+            # work around BufferedIO not being seekable
+            has_more = len(chunk) > 0
+            value = int.from_bytes(chunk, "little")
             for i, mask in enumerate(masks):
                 masked_value = value & mask
                 # Remove the zero padding, and scale it to 8 bits
-                data += o8(
-                    int(((masked_value >> mask_offsets[i]) / mask_totals[i]) * 255)
-                    if mask_totals[i]
-                    else 0
-                )
+                data += o8(int((masked_value >> mask_offsets[i]) * mask_totals[i]))
+
+        # extra padding pixels -- always all 0
+        if len(data) < dest_length:
+            pixel = bytearray()
+            pixel += o8(0)
+            ct_bytes = dest_length - len(data)
+            data += pixel * ct_bytes
+
         self.set_as_raw(data)
         return -1, 0