diff --git a/Tests/images/l2rgb_read.bmp b/Tests/images/l2rgb_read.bmp
new file mode 100644
index 000000000..838e3226b
Binary files /dev/null and b/Tests/images/l2rgb_read.bmp differ
diff --git a/Tests/test_map.py b/Tests/test_map.py
new file mode 100644
index 000000000..235bfadbc
--- /dev/null
+++ b/Tests/test_map.py
@@ -0,0 +1,25 @@
+from helper import PillowTestCase, unittest
+
+from PIL import Image
+
+class TestMap(PillowTestCase):
+    def test_overflow(self):
+        # There is the potential to overflow comparisons in map.c
+        # if there are > SIZE_MAX bytes in the image or if
+        # the file encodes an offset that makes
+        # (offset + size(bytes)) > SIZE_MAX
+
+        # Note that this image triggers the decompression bomb warning:
+        max_pixels = Image.MAX_IMAGE_PIXELS
+        Image.MAX_IMAGE_PIXELS = None
+
+        # This image hits the offset test.
+        im = Image.open('Tests/images/l2rgb_read.bmp')
+        with self.assertRaises((ValueError, MemoryError)):
+            im.load()
+
+        Image.MAX_IMAGE_PIXELS = max_pixels
+
+
+if __name__ == '__main__':
+    unittest.main()
diff --git a/map.c b/map.c
index 7309a7bd7..3637ee86a 100644
--- a/map.c
+++ b/map.c
@@ -342,8 +342,18 @@ PyImaging_MapBuffer(PyObject* self, PyObject* args)
             stride = xsize * 4;
     }
 
+    if (ysize > INT_MAX / stride) {
+        PyErr_SetString(PyExc_MemoryError, "Integer overflow in ysize");
+        return NULL;
+    }
+
     size = (Py_ssize_t) ysize * stride;
 
+    if (offset > SIZE_MAX - size) {
+        PyErr_SetString(PyExc_MemoryError, "Integer overflow in offset");
+        return NULL;
+    }        
+
     /* check buffer size */
     if (PyImaging_GetBuffer(target, &view) < 0)
         return NULL;