diff --git a/Lib/test/test_textwrap.py b/Lib/test/test_textwrap.py
index 7b72672..dccf095 100644
--- a/Lib/test/test_textwrap.py
+++ b/Lib/test/test_textwrap.py
@@ -647,6 +647,11 @@
         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))
+
 
 def test_main():
     test_support.run_unittest(WrapTestCase,
diff --git a/Lib/textwrap.py b/Lib/textwrap.py
index e755860..5c2e4fa 100644
--- a/Lib/textwrap.py
+++ b/Lib/textwrap.py
@@ -403,11 +403,15 @@
         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
+            for i, (x, y) in enumerate(zip(margin, indent)):
+                if x != y:
+                    margin = margin[:i]
+                    break
+            else:
+                margin = margin[:len(indent)]
 
     # sanity check (testing/debugging only)
     if 0 and margin: