diff --git a/Tests/test_j2k_overflow.py b/Tests/test_j2k_overflow.py
new file mode 100644
index 000000000..de671a53f
--- /dev/null
+++ b/Tests/test_j2k_overflow.py
@@ -0,0 +1,18 @@
+from PIL import Image
+from helper import unittest, PillowTestCase
+
+class TestJ2kEncodeOverflow(PillowTestCase):
+    def test_j2k_overflow(self):
+
+        im = Image.new('RGBA', (1024, 131584))
+        target = self.tempfile('temp.jpc')
+        try:
+            im.save(target)
+            self.assertTrue(False, "Expected IOError, save succeeded?")
+        except IOError as err:
+            self.assertTrue(True, "IOError is expected")
+        except Exception as err:
+            self.assertTrue(False, "Expected IOError, got %s" %type(err))
+
+if __name__ == '__main__':
+    unittest.main()
diff --git a/libImaging/Jpeg2KEncode.c b/libImaging/Jpeg2KEncode.c
index 3c6323eca..16f44f539 100644
--- a/libImaging/Jpeg2KEncode.c
+++ b/libImaging/Jpeg2KEncode.c
@@ -265,6 +265,10 @@ j2k_encode_entry(Imaging im, ImagingCodecState state,
 
     unsigned prec = 8;
     unsigned bpp = 8;
+    unsigned _overflow_scale_factor;
+    /* SIZE_MAX is not working in the conditionals unless it's a typed
+       variable */
+    unsigned _SIZE__MAX = SIZE_MAX;
 
     stream = opj_stream_default_create(OPJ_FALSE);
 
@@ -335,6 +339,11 @@ j2k_encode_entry(Imaging im, ImagingCodecState state,
     }
 
     image = opj_image_create(components, image_params, color_space);
+    if (!image) {
+        state->errcode = IMAGING_CODEC_BROKEN;
+        state->state = J2K_STATE_FAILED;
+        goto quick_exit;
+    }       
 
     /* Setup compression context */
     context->error_msg = NULL;
@@ -471,7 +480,24 @@ j2k_encode_entry(Imaging im, ImagingCodecState state,
     tiles_y = (im->ysize + (params.image_offset_y0 - params.cp_ty0)
                + tile_height - 1) / tile_height;
 
+    /* check for integer overflow for the malloc line, checking any expression
+       that may multiply either tile_width or tile_height */
+    _overflow_scale_factor = components * prec;
+    if (( tile_width > _SIZE__MAX / _overflow_scale_factor ) ||
+        ( tile_height > _SIZE__MAX / _overflow_scale_factor ) ||
+        ( tile_width > _SIZE__MAX / (tile_height * _overflow_scale_factor )) ||
+        ( tile_height > _SIZE__MAX / (tile_width * _overflow_scale_factor ))) {
+        state->errcode = IMAGING_CODEC_BROKEN;
+        state->state = J2K_STATE_FAILED;
+        goto quick_exit;
+    }
+    /* malloc check ok, checked for overflow above */
     state->buffer = malloc (tile_width * tile_height * components * prec / 8);
+    if (!state->buffer) {
+        state->errcode = IMAGING_CODEC_BROKEN;
+        state->state = J2K_STATE_FAILED;
+        goto quick_exit;
+    }
 
     tile_ndx = 0;
     for (y = 0; y < tiles_y; ++y) {