diff --git a/Tests/test_image_filter.py b/Tests/test_image_filter.py
index 3636a73f7..75665d20a 100644
--- a/Tests/test_image_filter.py
+++ b/Tests/test_image_filter.py
@@ -94,6 +94,15 @@ class TestImageFilter(PillowTestCase):
         self.assertEqual(rankfilter.size, 1)
         self.assertEqual(rankfilter.rank, 2)
 
+    def test_kernel_not_enough_coefficients(self):
+        self.assertRaises(ValueError,
+                          lambda: ImageFilter.Kernel((3, 3), (0, 0)))
+
+    def test_kernel_filter_p(self):
+        kernel = ImageFilter.Kernel((2, 2), (0, 0, 0, 0))
+
+        self.assertRaises(ValueError, kernel.filter, hopper("P"))
+
     def test_consistency_3x3(self):
         source = Image.open("Tests/images/hopper.bmp")
         reference = Image.open("Tests/images/hopper_emboss.bmp")