diff --git a/Tests/images/expected_to_read.jp2 b/Tests/images/expected_to_read.jp2
new file mode 100644
index 00000000000..d8029a0d3a0
Binary files /dev/null and b/Tests/images/expected_to_read.jp2 differ
diff --git a/Tests/images/invalid_header_length.jp2 b/Tests/images/invalid_header_length.jp2
new file mode 100644
index 00000000000..c0c14f42160
Binary files /dev/null and b/Tests/images/invalid_header_length.jp2 differ
diff --git a/Tests/images/not_enough_data.jp2 b/Tests/images/not_enough_data.jp2
new file mode 100644
index 00000000000..2d28bb5e96b
Binary files /dev/null and b/Tests/images/not_enough_data.jp2 differ
diff --git a/Tests/test_file_jpeg2k.py b/Tests/test_file_jpeg2k.py
index 779d246e930..db5288880db 100644
--- a/Tests/test_file_jpeg2k.py
+++ b/Tests/test_file_jpeg2k.py
@@ -4,7 +4,7 @@
 
 import pytest
 
-from PIL import Image, ImageFile, Jpeg2KImagePlugin, features
+from PIL import Image, ImageFile, Jpeg2KImagePlugin, UnidentifiedImageError, features
 
 from .helper import (
     assert_image_equal,
@@ -159,6 +159,20 @@ def test_load_dpi():
         assert "dpi" not in im.info
 
 
+def test_header_errors():
+    for path in (
+        "Tests/images/invalid_header_length.jp2",
+        "Tests/images/not_enough_data.jp2",
+    ):
+        with pytest.raises(UnidentifiedImageError):
+            with Image.open(path) as im:
+                pass
+
+    with pytest.raises(OSError):
+        with Image.open("Tests/images/expected_to_read.jp2") as im:
+            pass
+
+
 def test_layers_type(tmp_path):
     outfile = str(tmp_path / "temp_layers.jp2")
     for quality_layers in [[100, 50, 10], (100, 50, 10), None]: