diff --git a/django/utils/timezone.py b/django/utils/timezone.py
index 8138767fb2..0c44d4fd4d 100644
--- a/django/utils/timezone.py
+++ b/django/utils/timezone.py
@@ -306,9 +306,11 @@ def localtime(value, timezone=None):
     """
     if timezone is None:
         timezone = get_current_timezone()
+    # If `value` is naive, astimezone() will raise a ValueError,
+    # so we don't need to perform a redundant check.
     value = value.astimezone(timezone)
     if hasattr(timezone, 'normalize'):
-        # available for pytz time zones
+        # This method is available for pytz time zones.
         value = timezone.normalize(value)
     return value
 
@@ -351,13 +353,15 @@ def make_aware(value, timezone):
     """
     Makes a naive datetime.datetime in a given time zone aware.
     """
-    if is_aware(value):
-        raise ValueError("make_aware expects a naive value, got %s" % value)
     if hasattr(timezone, 'localize'):
-        # available for pytz time zones
+        # This method is available for pytz time zones.
         return timezone.localize(value, is_dst=None)
     else:
-        # may be wrong around DST changes
+        # Check that we won't overwrite the timezone of an aware datetime.
+        if is_aware(value):
+            raise ValueError(
+                    "make_aware expects a naive datetime, got %s" % value)
+        # This may be wrong around DST changes!
         return value.replace(tzinfo=timezone)
 
 
@@ -365,10 +369,10 @@ def make_naive(value, timezone):
     """
     Makes an aware datetime.datetime naive in a given time zone.
     """
-    if is_naive(value):
-        raise ValueError("make_naive expects an aware value, got %s" % value)
+    # If `value` is naive, astimezone() will raise a ValueError,
+    # so we don't need to perform a redundant check.
     value = value.astimezone(timezone)
     if hasattr(timezone, 'normalize'):
-        # available for pytz time zones
+        # This method is available for pytz time zones.
         value = timezone.normalize(value)
     return value.replace(tzinfo=None)
diff --git a/tests/timezones/tests.py b/tests/timezones/tests.py
index d16c7f7fd2..ab9ed6b1a1 100644
--- a/tests/timezones/tests.py
+++ b/tests/timezones/tests.py
@@ -1120,31 +1120,3 @@ class AdminTests(TestCase):
         with timezone.override(ICT):
             response = self.client.get(reverse('admin:timezones_timestamp_change', args=(t.pk,)))
         self.assertContains(response, t.created.astimezone(ICT).isoformat())
-
-
-@override_settings(TIME_ZONE='Africa/Nairobi')
-class UtilitiesTests(TestCase):
-
-    def test_make_aware(self):
-        self.assertEqual(
-            timezone.make_aware(datetime.datetime(2011, 9, 1, 13, 20, 30), EAT),
-            datetime.datetime(2011, 9, 1, 13, 20, 30, tzinfo=EAT)
-        )
-        self.assertEqual(
-            timezone.make_aware(datetime.datetime(2011, 9, 1, 10, 20, 30), UTC),
-            datetime.datetime(2011, 9, 1, 10, 20, 30, tzinfo=UTC)
-        )
-
-    def test_make_naive(self):
-        self.assertEqual(
-            timezone.make_naive(datetime.datetime(2011, 9, 1, 13, 20, 30, tzinfo=EAT), EAT),
-            datetime.datetime(2011, 9, 1, 13, 20, 30)
-        )
-        self.assertEqual(
-            timezone.make_naive(datetime.datetime(2011, 9, 1, 13, 20, 30, tzinfo=EAT), UTC),
-            datetime.datetime(2011, 9, 1, 10, 20, 30)
-        )
-        self.assertEqual(
-            timezone.make_naive(datetime.datetime(2011, 9, 1, 10, 20, 30, tzinfo=UTC), UTC),
-            datetime.datetime(2011, 9, 1, 10, 20, 30)
-        )
diff --git a/tests/utils_tests/test_timezone.py b/tests/utils_tests/test_timezone.py
index 4b5a39a928..aec58e394f 100644
--- a/tests/utils_tests/test_timezone.py
+++ b/tests/utils_tests/test_timezone.py
@@ -3,10 +3,17 @@ import datetime
 import pickle
 import unittest
 
+try:
+    import pytz
+except ImportError:
+    pytz = None
+
 from django.test import override_settings
 from django.utils import timezone
 
 
+if pytz is not None:
+    CET = pytz.timezone("Europe/Paris")
 EAT = timezone.get_fixed_timezone(180)      # Africa/Nairobi
 ICT = timezone.get_fixed_timezone(420)      # Asia/Bangkok
 
@@ -19,6 +26,10 @@ class TimezoneTests(unittest.TestCase):
         local_now = timezone.localtime(now, local_tz)
         self.assertEqual(local_now.tzinfo, local_tz)
 
+    def test_localtime_naive(self):
+        with self.assertRaises(ValueError):
+            timezone.localtime(datetime.datetime.now())
+
     def test_localtime_out_of_range(self):
         local_tz = timezone.LocalTimezone()
         long_ago = datetime.datetime(1900, 1, 1, tzinfo=timezone.utc)
@@ -96,3 +107,22 @@ class TimezoneTests(unittest.TestCase):
             datetime.datetime(2011, 9, 1, 13, 20, 30))
         with self.assertRaises(ValueError):
             timezone.make_naive(datetime.datetime(2011, 9, 1, 13, 20, 30), EAT)
+
+    @unittest.skipIf(pytz is None, "this test requires pytz")
+    def test_make_aware(self):
+        self.assertEqual(
+            timezone.make_aware(datetime.datetime(2011, 9, 1, 12, 20, 30), CET),
+            CET.localize(datetime.datetime(2011, 9, 1, 12, 20, 30)))
+        with self.assertRaises(ValueError):
+            timezone.make_aware(CET.localize(datetime.datetime(2011, 9, 1, 12, 20, 30)), CET)
+
+    @unittest.skipIf(pytz is None, "this test requires pytz")
+    def test_make_aware_pytz(self):
+        self.assertEqual(
+            timezone.make_naive(CET.localize(datetime.datetime(2011, 9, 1, 12, 20, 30)), CET),
+            datetime.datetime(2011, 9, 1, 12, 20, 30))
+        self.assertEqual(
+            timezone.make_naive(pytz.timezone("Asia/Bangkok").localize(datetime.datetime(2011, 9, 1, 17, 20, 30)), CET),
+            datetime.datetime(2011, 9, 1, 12, 20, 30))
+        with self.assertRaises(ValueError):
+            timezone.make_naive(datetime.datetime(2011, 9, 1, 12, 20, 30), CET)