diff --git a/src/PIL/JpegImagePlugin.py b/src/PIL/JpegImagePlugin.py
index 475e54c2b..fe921eb65 100644
--- a/src/PIL/JpegImagePlugin.py
+++ b/src/PIL/JpegImagePlugin.py
@@ -800,7 +800,7 @@ def _save(im, fp, filename):
 
     # The EXIF info needs to be written as one block, + APP1, + one spare byte.
     # Ensure that our buffer is big enough. Same with the icc_profile block.
-    bufsize = max(ImageFile.MAXBLOCK, bufsize, len(exif) + 5, len(extra) + 1)
+    bufsize = max(bufsize, len(exif) + 5, len(extra) + 1)
 
     ImageFile._save(im, fp, [("jpeg", (0, 0) + im.size, 0, rawmode)], bufsize)