diff --git a/tests/gis_tests/geoapp/test_functions.py b/tests/gis_tests/geoapp/test_functions.py
index 3d809927b9..a2c172b001 100644
--- a/tests/gis_tests/geoapp/test_functions.py
+++ b/tests/gis_tests/geoapp/test_functions.py
@@ -485,8 +485,5 @@ class GISFunctionsTests(TestCase):
     def test_union(self):
         geom = Point(-95.363151, 29.763374, srid=4326)
         ptown = City.objects.annotate(union=functions.Union('point', geom)).get(name='Dallas')
-        tol = 0.00001
-        # Undefined ordering
-        expected1 = fromstr('MULTIPOINT(-96.801611 32.782057,-95.363151 29.763374)', srid=4326)
-        expected2 = fromstr('MULTIPOINT(-95.363151 29.763374,-96.801611 32.782057)', srid=4326)
-        self.assertTrue(expected1.equals_exact(ptown.union, tol) or expected2.equals_exact(ptown.union, tol))
+        expected = fromstr('MULTIPOINT(-96.801611 32.782057,-95.363151 29.763374)', srid=4326)
+        self.assertTrue(expected.equals(ptown.union))
diff --git a/tests/gis_tests/geoapp/tests.py b/tests/gis_tests/geoapp/tests.py
index 536aa1b907..074162fe14 100644
--- a/tests/gis_tests/geoapp/tests.py
+++ b/tests/gis_tests/geoapp/tests.py
@@ -858,8 +858,7 @@ class GeoQuerySetTest(TestCase):
         """
         tx = Country.objects.get(name='Texas').mpoly
         # Houston, Dallas -- Ordering may differ depending on backend or GEOS version.
-        union1 = fromstr('MULTIPOINT(-96.801611 32.782057,-95.363151 29.763374)')
-        union2 = fromstr('MULTIPOINT(-95.363151 29.763374,-96.801611 32.782057)')
+        union = GEOSGeometry('MULTIPOINT(-96.801611 32.782057,-95.363151 29.763374)')
         qs = City.objects.filter(point__within=tx)
         with self.assertRaises(ValueError):
             qs.aggregate(Union('name'))
@@ -868,9 +867,8 @@ class GeoQuerySetTest(TestCase):
         # an aggregate method on a spatial column)
         u1 = qs.aggregate(Union('point'))['point__union']
         u2 = qs.order_by('name').aggregate(Union('point'))['point__union']
-        tol = 0.00001
-        self.assertTrue(union1.equals_exact(u1, tol) or union2.equals_exact(u1, tol))
-        self.assertTrue(union1.equals_exact(u2, tol) or union2.equals_exact(u2, tol))
+        self.assertTrue(union.equals(u1))
+        self.assertTrue(union.equals(u2))
         qs = City.objects.filter(name='NotACity')
         self.assertIsNone(qs.aggregate(Union('point'))['point__union'])