diff --git a/.github/workflows/test-valgrind.yml b/.github/workflows/test-valgrind.yml
index 219189cf208..f8b050f7625 100644
--- a/.github/workflows/test-valgrind.yml
+++ b/.github/workflows/test-valgrind.yml
@@ -48,5 +48,5 @@ jobs:
       run: |
         # The Pillow user in the docker container is UID 1000
         sudo chown -R 1000 $GITHUB_WORKSPACE
-        docker run --name pillow_container  -v $GITHUB_WORKSPACE:/Pillow pythonpillow/${{ matrix.docker }}:${{ matrix.dockerTag }}
+        docker run --name pillow_container -e "PILLOW_VALGRIND_TEST=true" -v $GITHUB_WORKSPACE:/Pillow pythonpillow/${{ matrix.docker }}:${{ matrix.dockerTag }}
         sudo chown -R runner $GITHUB_WORKSPACE
diff --git a/Tests/test_file_pdf.py b/Tests/test_file_pdf.py
index 9667b6a4aad..5299febe915 100644
--- a/Tests/test_file_pdf.py
+++ b/Tests/test_file_pdf.py
@@ -286,6 +286,7 @@ def test_pdf_append_to_bytesio():
 
 
 @pytest.mark.timeout(1)
+@pytest.mark.skipif("PILLOW_VALGRIND_TEST" in os.environ, reason="Valgrind is slower")
 @pytest.mark.parametrize("newline", (b"\r", b"\n"))
 def test_redos(newline):
     malicious = b" trailer<<>>" + newline * 3456
diff --git a/Tests/test_image.py b/Tests/test_image.py
index a0c50b5f407..d261638f941 100644
--- a/Tests/test_image.py
+++ b/Tests/test_image.py
@@ -512,6 +512,14 @@ def test_check_size(self):
         i = Image.new("RGB", [1, 1])
         assert isinstance(i.size, tuple)
 
+    @pytest.mark.timeout(0.75)
+    @pytest.mark.skipif(
+        "PILLOW_VALGRIND_TEST" in os.environ, reason="Valgrind is slower"
+    )
+    @pytest.mark.parametrize("size", ((0, 100000000), (100000000, 0)))
+    def test_empty_image(self, size):
+        Image.new("RGB", size)
+
     def test_storage_neg(self):
         # Storage.c accepted negative values for xsize, ysize.  Was
         # test_neg_ppm, but the core function for that has been
diff --git a/src/libImaging/Fill.c b/src/libImaging/Fill.c
index f7206022843..5b6bfb89cd8 100644
--- a/src/libImaging/Fill.c
+++ b/src/libImaging/Fill.c
@@ -24,6 +24,11 @@ ImagingFill(Imaging im, const void *colour) {
     int x, y;
     ImagingSectionCookie cookie;
 
+    /* 0-width or 0-height image. No need to do anything */
+    if (!im->linesize || !im->ysize) {
+        return im;
+    }
+
     if (im->type == IMAGING_TYPE_SPECIAL) {
         /* use generic API */
         ImagingAccess access = ImagingAccessNew(im);