~/py27 $ hg diff
diff --git a/Lib/random.py b/Lib/random.py
--- a/Lib/random.py
+++ b/Lib/random.py
@@ -290,6 +290,24 @@
             j = _int(random() * (i+1))
             x[i], x[j] = x[j], x[i]
 
+    def shuffle_min(self, x, random=None):
+        if random is None:
+            random = self.random
+        _int = int
+        _min = min
+        for i in reversed(xrange(1, len(x))):
+            j = _min(_int(random() * (i+1)), i)
+            x[i], x[j] = x[j], x[i]
+
+    def shuffle_eq(self, x, random=None):
+        if random is None:
+            random = self.random
+        _int = int
+        for i in reversed(xrange(1, len(x))):
+            j = _int(random() * (i+1))
+            if j != i+1:
+                x[i], x[j] = x[j], x[i]
+
     def sample(self, population, k):
         """Chooses k unique random elements from a population sequence.
 
~/py27 $ py27 -m timeit -s 'import random' -s 'shuffle=random.Random(8675309).shuffle' -s 'seq = range(10000)' 'shuffle(seq)'
100 loops, best of 3: 2.69 msec per loop
~/py27 $ py27 -m timeit -s 'import random' -s 'shuffle=random.Random(8675309).shuffle_min' -s 'seq = range(10000)' 'shuffle(seq)'
100 loops, best of 3: 3.76 msec per loop
~/py27 $ py27 -m timeit -s 'import random' -s 'shuffle=random.Random(8675309).shuffle_eq' -s 'seq = range(10000)' 'shuffle(seq)'
100 loops, best of 3: 3.01 msec per loop
~/py27 $ 
~/py27 $ py27 -m timeit -s 'import random' -s 'shuffle=random.Random(8675309).shuffle' -s 'seq = range(10000)' 'shuffle(seq)'
100 loops, best of 3: 2.69 msec per loop
~/py27 $ py27 -m timeit -s 'import random' -s 'shuffle=random.Random(8675309).shuffle_min' -s 'seq = range(10000)' 'shuffle(seq)'
100 loops, best of 3: 3.82 msec per loop
~/py27 $ py27 -m timeit -s 'import random' -s 'shuffle=random.Random(8675309).shuffle_eq' -s 'seq = range(10000)' 'shuffle(seq)'
100 loops, best of 3: 3.01 msec per loop
~/py27 $ 
~/py27 $ cp Lib/random.py random.py
~/py27 $ pypy -m timeit -s 'import random' -s 'shuffle=random.Random(8675309).shuffle' -s 'seq = range(10000)' 'shuffle(seq)'
10000 loops, best of 3: 155 usec per loop
~/py27 $ pypy -m timeit -s 'import random' -s 'shuffle=random.Random(8675309).shuffle_min' -s 'seq = range(10000)' 'shuffle(seq)'
10000 loops, best of 3: 152 usec per loop
~/py27 $ pypy -m timeit -s 'import random' -s 'shuffle=random.Random(8675309).shuffle_eq' -s 'seq = range(10000)' 'shuffle(seq)'
10000 loops, best of 3: 160 usec per loop
~/py27 $ 
~/py27 $ pypy -m timeit -s 'import random' -s 'shuffle=random.Random(8675309).shuffle' -s 'seq = range(10000)' 'shuffle(seq)'
10000 loops, best of 3: 155 usec per loop
~/py27 $ pypy -m timeit -s 'import random' -s 'shuffle=random.Random(8675309).shuffle_min' -s 'seq = range(10000)' 'shuffle(seq)'
10000 loops, best of 3: 152 usec per loop
~/py27 $ pypy -m timeit -s 'import random' -s 'shuffle=random.Random(8675309).shuffle_eq' -s 'seq = range(10000)' 'shuffle(seq)'
10000 loops, best of 3: 160 usec per loop