diff --git a/Tests/test_file_sgi.py b/Tests/test_file_sgi.py
index c9aeea76c..a535a1730 100644
--- a/Tests/test_file_sgi.py
+++ b/Tests/test_file_sgi.py
@@ -55,6 +55,22 @@ class TestFileSgi(PillowTestCase):
         for mode in ('L', 'RGB', 'RGBA'):
             roundtrip(hopper(mode))
 
+        # Test 1 dimension for an L mode image
+        roundtrip(Image.new('L', (10, 1)))
+
+    def test_unsupported_mode(self):
+        im = hopper('LA')
+        out = self.tempfile('temp.sgi')
+
+        self.assertRaises(ValueError, lambda: im.save(out, format='sgi'))
+
+    def test_incorrect_number_of_bands(self):
+        im = hopper('YCbCr')
+        im.mode = 'RGB'
+        out = self.tempfile('temp.sgi')
+
+        self.assertRaises(ValueError, lambda: im.save(out, format='sgi'))
+
 
 if __name__ == '__main__':
     unittest.main()