diff --git a/PIL/ImageFilter.py b/PIL/ImageFilter.py
index 6d328cc1a..cfdad5fc5 100644
--- a/PIL/ImageFilter.py
+++ b/PIL/ImageFilter.py
@@ -15,6 +15,8 @@
 # See the README file for information on usage and redistribution.
 #
 
+from functools import reduce
+
 class Filter:
     pass
 
diff --git a/PIL/ImageOps.py b/PIL/ImageOps.py
index 9825d9ced..de32726a1 100644
--- a/PIL/ImageOps.py
+++ b/PIL/ImageOps.py
@@ -19,6 +19,7 @@
 
 import Image
 import operator
+from functools import reduce
 
 ##
 # (New in 1.1.3) The <b>ImageOps</b> module contains a number of
diff --git a/PIL/ImageStat.py b/PIL/ImageStat.py
index 7ab258c1a..c87bd57cb 100644
--- a/PIL/ImageStat.py
+++ b/PIL/ImageStat.py
@@ -23,6 +23,7 @@
 
 import Image
 import operator, math
+from functools import reduce
 
 ##
 # The <b>ImageStat</b> module calculates global statistics for an