diff --git a/tests/syndication/tests.py b/tests/syndication/tests.py
index 1627f71..828de7a 100644
--- a/tests/syndication/tests.py
+++ b/tests/syndication/tests.py
@@ -1,5 +1,6 @@
 from __future__ import absolute_import, unicode_literals
 
+import time
 from xml.dom import minidom
 
 from django.contrib.syndication import views
@@ -7,10 +8,24 @@ from django.core.exceptions import ImproperlyConfigured
 from django.test import TestCase
 from django.utils import tzinfo
 from django.utils.feedgenerator import rfc2822_date, rfc3339_date
+from django.utils.unittest import skipUnless
 
 from .models import Entry
 
 
+# Taken from tests/timezones/tests.py
+TZ_SUPPORT = hasattr(time, 'tzset')
+
+# On OSes that don't provide tzset (Windows), we can't set the timezone
+# in which the program runs. As a consequence, we must skip tests that
+# don't enforce a specific timezone (with timezone.override or equivalent),
+# or attempt to interpret naive datetimes in the default timezone.
+
+requires_tz_support = skipUnless(TZ_SUPPORT,
+        "This test relies on the ability to run a program in an arbitrary "
+        "time zone, but your operating system isn't able to do that.")
+
+
 class FeedTestCase(TestCase):
     fixtures = ['feeddata.json']
 
@@ -260,10 +275,18 @@ class SyndicationFeedTest(FeedTestCase):
         updated = doc.getElementsByTagName('updated')[0].firstChild.wholeText
         self.assertEqual(updated[-6:], '+00:42')
 
-    def test_feed_last_modified_time(self):
+    @requires_tz_support
+    def test_feed_last_modified_time_naive_date(self):
+        """
+        Tests the Last-Modified header with naive publication dates
+        """
         response = self.client.get('/syndication/naive-dates/')
         self.assertEqual(response['Last-Modified'], 'Thu, 03 Jan 2008 19:30:00 GMT')
 
+    def test_feed_last_modified_time(self):
+        response = self.client.get('/syndication/aware-dates/')
+        self.assertEqual(response['Last-Modified'], 'Thu, 03 Jan 2008 12:48:00 GMT')
+
         # No last-modified when feed has no item_pubdate
         response = self.client.get('/syndication/no_pubdate/')
         self.assertFalse(response.has_header('Last-Modified'))