diff --git a/Tests/helper.py b/Tests/helper.py
index 1ede4b7d5b1..cd2c9b71f39 100644
--- a/Tests/helper.py
+++ b/Tests/helper.py
@@ -10,6 +10,7 @@
 import subprocess
 import sys
 import tempfile
+import time
 from functools import lru_cache
 from io import BytesIO
 
@@ -339,3 +340,17 @@ def is_ppc64le() -> bool:
 
 def is_win32() -> bool:
     return sys.platform.startswith("win32")
+
+
+def measure_cpu_seconds(f: Callable[[], Any], times: int = 3) -> float:
+    """
+    Measure the execution time of a function.
+    """
+    best = float("inf")
+    for _ in range(times):
+        # `process_time` is the sum of the system and user CPU time
+        # of the current process, not wallclock time.
+        start = time.process_time()
+        f()
+        best = min(best, time.process_time() - start)
+    return best
diff --git a/Tests/test_image.py b/Tests/test_image.py
index d0516b849f2..ecc21c1736f 100644
--- a/Tests/test_image.py
+++ b/Tests/test_image.py
@@ -30,8 +30,8 @@
     hopper,
     is_win32,
     mark_if_feature_version,
+    measure_cpu_seconds,
     skip_unless_feature,
-    timeout_unless_slower_valgrind,
 )
 
 TYPE_CHECKING = False
@@ -571,12 +571,18 @@ def test_check_size(self) -> None:
         i = Image.new("RGB", [1, 1])
         assert isinstance(i.size, tuple)
 
-    @timeout_unless_slower_valgrind(0.75)
     @pytest.mark.parametrize(
-        "size", ((0, 10_000_000), (10_000_000, 0)), ids=("tall", "wide")
+        "size", ((0, 100_000_000), (100_000_000, 0)), ids=("tall", "wide")
     )
     def test_empty_image(self, size: tuple[int, int]) -> None:
-        Image.new("RGB", size)
+        # Test that initializing an empty image does not do
+        # extra work to try and fill the image.
+        # Allocating a tall image can still take a while
+        # since the internal row pointers are necessarily allocated,
+        # so measure the difference between doing that work and not doing it.
+        unfilled = measure_cpu_seconds(lambda: Image.new("RGB", size, None))
+        filled = measure_cpu_seconds(lambda: Image.new("RGB", size, 0))
+        assert filled - unfilled < 0.1
 
     def test_storage_neg(self) -> None:
         # Storage.c accepted negative values for xsize, ysize.  Was