diff --git a/PIL/JpegImagePlugin.py b/PIL/JpegImagePlugin.py
index 90d3b5194..9563f9723 100644
--- a/PIL/JpegImagePlugin.py
+++ b/PIL/JpegImagePlugin.py
@@ -566,7 +566,10 @@ def _save(im, fp, filename):
     # https://github.com/jdriscoll/django-imagekit/issues/50
     bufsize=0
     if "optimize" in info or "progressive" in info or "progression" in info:
-        bufsize = im.size[0]*im.size[1]
+        if quality >= 95:
+            bufsize = 2 * im.size[0] * im.size[1]
+        else:
+            bufsize = im.size[0] * im.size[1]
 
     # The exif info needs to be written as one block, + APP1, + one spare byte.
     # Ensure that our buffer is big enough
diff --git a/Tests/test_file_jpeg.py b/Tests/test_file_jpeg.py
index de1c3f0e1..de91c2b63 100644
--- a/Tests/test_file_jpeg.py
+++ b/Tests/test_file_jpeg.py
@@ -1,5 +1,8 @@
 from tester import *
 
+import array
+import random
+
 from PIL import Image
 from PIL import ImageFile
 
@@ -132,13 +135,21 @@ def test_progressive_large_buffer():
     im = Image.new("RGB", (4096,4096), 0xff3333)
     im.save(f, format="JPEG", progressive=True)
 
+def test_progressive_large_buffer_highest_quality():
+    f = tempfile('temp.jpg')
+    a = array.array('B')
+    a.extend(random.randint(0, 255) for _ in xrange(256 * 256 * 3))
+    im = Image.frombuffer("RGB", (256, 256), a, "raw", "RGB", 0, 1)
+    # this requires more bytes than pixels in the image
+    im.save(f, format="JPEG", progressive=True, quality=100)
+
 def test_large_exif():
     #https://github.com/python-imaging/Pillow/issues/148
     f = tempfile('temp.jpg')
     im = lena()
     im.save(f,'JPEG', quality=90, exif=b"1"*65532)
 
-def test_progressive():
+def test_progressive_compat():
     im1 = roundtrip(lena())
     im2 = roundtrip(lena(), progressive=1)
     im3 = roundtrip(lena(), progression=1) # compatibility