diff --git a/Lib/test/datetimetester.py b/Lib/test/datetimetester.py
index a7e5e0b..7d4cdac 100644
--- a/Lib/test/datetimetester.py
+++ b/Lib/test/datetimetester.py
@@ -2414,25 +2414,24 @@
         base = cls(2000, 2, 29)
         self.assertRaises(ValueError, base.replace, year=2001)
 
+    @support.run_with_tz('EDT4')
     def test_astimezone(self):
-        return  # The rest is no longer applicable
-        # Pretty boring!  The TZ test is more interesting here.  astimezone()
-        # simply can't be applied to a naive object.
         dt = self.theclass.now()
-        f = FixedOffset(44, "")
-        self.assertRaises(ValueError, dt.astimezone) # naive
+        f = FixedOffset(44, "0044")
+        dt_utc = dt.replace(tzinfo=timezone(timedelta(hours=-4), 'EDT'))
+        self.assertEqual(dt.astimezone(), dt_utc) # naive
         self.assertRaises(TypeError, dt.astimezone, f, f) # too many args
         self.assertRaises(TypeError, dt.astimezone, dt) # arg wrong type
-        self.assertRaises(ValueError, dt.astimezone, f) # naive
-        self.assertRaises(ValueError, dt.astimezone, tz=f)  # naive
+        dt_f = dt.replace(tzinfo=f) + timedelta(hours=4, minutes=44)
+        self.assertEqual(dt.astimezone(f), dt_f) # naive
+        self.assertEqual(dt.astimezone(tz=f), dt_f) # naive
 
         class Bogus(tzinfo):
             def utcoffset(self, dt): return None
             def dst(self, dt): return timedelta(0)
         bog = Bogus()
         self.assertRaises(ValueError, dt.astimezone, bog)   # naive
-        self.assertRaises(ValueError,
-                          dt.replace(tzinfo=bog).astimezone, f)
+        self.assertEqual(dt.replace(tzinfo=bog).astimezone(f), dt_f)
 
         class AlsoBogus(tzinfo):
             def utcoffset(self, dt): return timedelta(0)
@@ -2440,6 +2439,14 @@
         alsobog = AlsoBogus()
         self.assertRaises(ValueError, dt.astimezone, alsobog) # also naive
 
+        class Broken(tzinfo):
+            def utcoffset(self, dt): return 1
+            def dst(self, dt): return 1
+        broken = Broken()
+        dt_broken = dt.replace(tzinfo=broken)
+        with self.assertRaises(TypeError):
+            dt_broken.astimezone()
+
     def test_subclass_datetime(self):
 
         class C(self.theclass):