diff --git a/PIL/JpegImagePlugin.py b/PIL/JpegImagePlugin.py
index 6d4e588c017..2728fb9f89f 100644
--- a/PIL/JpegImagePlugin.py
+++ b/PIL/JpegImagePlugin.py
@@ -341,6 +341,10 @@ def draft(self, mode, size):
         if len(self.tile) != 1:
             return
 
+        # Protect from second call
+        if self.decoderconfig:
+            return
+
         d, e, o, a = self.tile[0]
         scale = 0
 
@@ -349,7 +353,7 @@ def draft(self, mode, size):
             a = mode, ""
 
         if size:
-            scale = max(self.size[0] // size[0], self.size[1] // size[1])
+            scale = min(self.size[0] // size[0], self.size[1] // size[1])
             for s in [8, 4, 2, 1]:
                 if scale >= s:
                     break
diff --git a/Tests/test_image_draft.py b/Tests/test_image_draft.py
index 0a8cc023c77..12f5e0e9f38 100644
--- a/Tests/test_image_draft.py
+++ b/Tests/test_image_draft.py
@@ -2,36 +2,73 @@
 
 from PIL import Image
 
-CODECS = dir(Image.core)
-FILENAME = "Tests/images/hopper.jpg"
-DATA = tostring(Image.open(FILENAME).resize((512, 512)), "JPEG")
-
-
-def draft(mode, size):
-    im = fromstring(DATA)
-    im.draft(mode, size)
-    return im
-
 
 class TestImageDraft(PillowTestCase):
-
     def setUp(self):
-        if "jpeg_encoder" not in CODECS or "jpeg_decoder" not in CODECS:
+        codecs = dir(Image.core)
+        if "jpeg_encoder" not in codecs or "jpeg_decoder" not in codecs:
             self.skipTest("jpeg support not available")
 
+    def draft_roundtrip(self, in_mode, in_size, req_mode, req_size):
+        im = Image.new(in_mode, in_size)
+        data = tostring(im, 'JPEG')
+        im = fromstring(data)
+        im.draft(req_mode, req_size)
+        return im
+
     def test_size(self):
-        self.assertEqual(draft("RGB", (512, 512)).size, (512, 512))
-        self.assertEqual(draft("RGB", (256, 256)).size, (256, 256))
-        self.assertEqual(draft("RGB", (128, 128)).size, (128, 128))
-        self.assertEqual(draft("RGB", (64, 64)).size, (64, 64))
-        self.assertEqual(draft("RGB", (32, 32)).size, (64, 64))
+        for in_size, req_size, out_size in [
+            ((435, 361), (2048, 2048), (435, 361)),  # bigger
+            ((435, 361), (435, 361), (435, 361)),  # same
+            ((128, 128), (64, 64), (64, 64)),
+            ((128, 128), (32, 32), (32, 32)),
+            ((128, 128), (16, 16), (16, 16)),
+
+            # large requested width
+            ((435, 361), (218, 128), (435, 361)),  # almost 2x
+            ((435, 361), (217, 128), (218, 181)),  # more than 2x
+            ((435, 361), (109, 64), (218, 181)),  # almost 4x
+            ((435, 361), (108, 64), (109, 91)),  # more than 4x
+            ((435, 361), (55, 32), (109, 91)),  # almost 8x
+            ((435, 361), (54, 32), (55, 46)),  # more than 8x
+            ((435, 361), (27, 16), (55, 46)),  # more than 16x
+
+            # and vice versa
+            ((435, 361), (128, 181), (435, 361)),  # almost 2x
+            ((435, 361), (128, 180), (218, 181)),  # more than 2x
+            ((435, 361), (64, 91), (218, 181)),  # almost 4x
+            ((435, 361), (64, 90), (109, 91)),  # more than 4x
+            ((435, 361), (32, 46), (109, 91)),  # almost 8x
+            ((435, 361), (32, 45), (55, 46)),  # more than 8x
+            ((435, 361), (16, 22), (55, 46)),  # more than 16x
+        ]:
+            im = self.draft_roundtrip('L', in_size, None, req_size)
+            im.load()
+            self.assertEqual(im.size, out_size)
 
     def test_mode(self):
-        self.assertEqual(draft("1", (512, 512)).mode, "RGB")
-        self.assertEqual(draft("L", (512, 512)).mode, "L")
-        self.assertEqual(draft("RGB", (512, 512)).mode, "RGB")
-        self.assertEqual(draft("YCbCr", (512, 512)).mode, "YCbCr")
+        for in_mode, req_mode, out_mode in [
+            ("RGB", "1", "RGB"),
+            ("RGB", "L", "L"),
+            ("RGB", "RGB", "RGB"),
+            ("RGB", "YCbCr", "YCbCr"),
+            ("L", "1", "L"),
+            ("L", "L", "L"),
+            ("L", "RGB", "L"),
+            ("L", "YCbCr", "L"),
+            ("CMYK", "1", "CMYK"),
+            ("CMYK", "L", "CMYK"),
+            ("CMYK", "RGB", "CMYK"),
+            ("CMYK", "YCbCr", "CMYK"),
+        ]:
+            im = self.draft_roundtrip(in_mode, (64, 64), req_mode, None)
+            im.load()
+            self.assertEqual(im.mode, out_mode)
 
+    def test_several_drafts(self):
+        im = self.draft_roundtrip('L', (128, 128), None, (64, 64))
+        im.draft(None, (64, 64))
+        im.load()
 
 if __name__ == '__main__':
     unittest.main()