diff -r fdfa15a9243c -r 34e88a05562f Lib/test/test_textwrap.py
--- a/Lib/test/test_textwrap.py	Sat Jun 21 13:59:25 2014 +0200
+++ b/Lib/test/test_textwrap.py	Sun Jun 22 14:35:10 2014 -0400
@@ -732,6 +732,11 @@
         expect = "hello there\n  how are you?"
         self.assertEqual(expect, dedent(text))
 
+        # test margin is smaller than smallest indent
+        text = "  \thello there\n   \thow are you?\n \tI'm fine, thanks"
+        expect = " \thello there\n  \thow are you?\n\tI'm fine, thanks"
+        self.assertEqual(expect, dedent(text))
+
 
 # Test textwrap.indent
 class IndentTestCase(unittest.TestCase):
diff -r fdfa15a9243c -r 34e88a05562f Lib/textwrap.py
--- a/Lib/textwrap.py	Sat Jun 21 13:59:25 2014 +0200
+++ b/Lib/textwrap.py	Sun Jun 22 14:35:10 2014 -0400
@@ -429,11 +429,16 @@
         elif margin.startswith(indent):
             margin = indent
 
-        # Current line and previous winner have no common whitespace:
-        # there is no margin.
+        # Find the largest common whitespace between current line and previous
+        # winner.
         else:
-            margin = ""
-            break
+            matches = [x == y for x, y in zip(margin, indent)]
+            result = ""
+            i = 0
+            while matches[i]:
+                result += margin[i]
+                i += 1
+            margin = result
 
     # sanity check (testing/debugging only)
     if 0 and margin: