diff --git a/Tests/images/ico1both.ico b/Tests/images/ico1both.ico
new file mode 100644
index 000000000..d0c95b70c
Binary files /dev/null and b/Tests/images/ico1both.ico differ
diff --git a/Tests/images/ico1device_dependent.ico b/Tests/images/ico1device_dependent.ico
new file mode 100644
index 000000000..8a6a9f2e0
Binary files /dev/null and b/Tests/images/ico1device_dependent.ico differ
diff --git a/Tests/images/ico1.ico b/Tests/images/ico1device_independent.ico
similarity index 100%
rename from Tests/images/ico1.ico
rename to Tests/images/ico1device_independent.ico
diff --git a/Tests/test_file_ico.py b/Tests/test_file_ico.py
index 7c5dd0739..e4b8bd62a 100644
--- a/Tests/test_file_ico.py
+++ b/Tests/test_file_ico.py
@@ -229,10 +229,20 @@ def test_draw_reloaded(tmp_path):
         assert_image_equal_tofile(im, "Tests/images/hopper_draw.ico")
 
 
-def test_ico1_open():
-    with Image.open("Tests/images/ico1.ico") as im:
+@pytest.mark.parametrize(
+    "test_image_path",
+    (
+        "Tests/images/ico1device_independent.ico",
+        "Tests/images/ico1device_dependent.ico",
+        "Tests/images/ico1both.ico",
+    ),
+)
+def test_ico1_open(test_image_path):
+    with Image.open(test_image_path) as im:
         assert_image_equal_tofile(im, "Tests/images/ico1.png")
 
+
+def test_ico1_invalid_file():
     with open("Tests/images/flower.jpg", "rb") as fp:
         with pytest.raises(SyntaxError):
             IcoImagePlugin.Ico1ImageFile(fp)
diff --git a/docs/handbook/image-file-formats.rst b/docs/handbook/image-file-formats.rst
index d92978c4a..ca980a764 100644
--- a/docs/handbook/image-file-formats.rst
+++ b/docs/handbook/image-file-formats.rst
@@ -345,7 +345,8 @@ The :py:meth:`~PIL.Image.Image.save` method can take the following keyword argum
 ICO1
 ^^^^
 
-Pillow also reads and writes device-independent Windows 1.0 icons.
+Pillow also reads Windows 1.0 icons in all three formats ("Device-Independent",
+"Device-Dependent" and "Both"), and writes them in "Device-Independent" format.
 
 .. versionadded:: 10.1.0
 
diff --git a/src/PIL/IcoImagePlugin.py b/src/PIL/IcoImagePlugin.py
index 534708024..d1a88f396 100644
--- a/src/PIL/IcoImagePlugin.py
+++ b/src/PIL/IcoImagePlugin.py
@@ -349,7 +349,7 @@ class IcoImageFile(ImageFile.ImageFile):
 
 
 def _ico1_accept(prefix):
-    return prefix[:2] == b"\1\0"
+    return prefix[0] == 1 and prefix[1] in (0, 1, 2)
 
 
 class Ico1ImageFile(ImageFile.ImageFile):