diff --git a/django/contrib/gis/tests/geoapp/tests.py b/django/contrib/gis/tests/geoapp/tests.py
index 574cc8fff6..6533319885 100644
--- a/django/contrib/gis/tests/geoapp/tests.py
+++ b/django/contrib/gis/tests/geoapp/tests.py
@@ -155,21 +155,22 @@ class GeoModelTest(unittest.TestCase):
         # Pre-transformed points for Houston and Pueblo.
         htown = fromstr('POINT(1947516.83115183 6322297.06040572)', srid=3084)
         ptown = fromstr('POINT(992363.390841912 481455.395105533)', srid=2774)
+        prec = 3 # Precision is low due to version variations in PROJ and GDAL.
 
         # Asserting the result of the transform operation with the values in
         #  the pre-transformed points.  Oracle does not have the 3084 SRID.
         if not oracle:
             h = City.objects.transform('point', srid=htown.srid).get(name='Houston')
             self.assertEqual(3084, h.point.srid)
-            self.assertAlmostEqual(htown.x, h.point.x, 8)
-            self.assertAlmostEqual(htown.y, h.point.y, 8)
+            self.assertAlmostEqual(htown.x, h.point.x, prec)
+            self.assertAlmostEqual(htown.y, h.point.y, prec)
 
         p1 = City.objects.transform('point', srid=ptown.srid).get(name='Pueblo')
         p2 = City.objects.transform(srid=ptown.srid).get(name='Pueblo')
         for p in [p1, p2]:
             self.assertEqual(2774, p.point.srid)
-            self.assertAlmostEqual(ptown.x, p.point.x, 7)
-            self.assertAlmostEqual(ptown.y, p.point.y, 7)
+            self.assertAlmostEqual(ptown.x, p.point.x, prec)
+            self.assertAlmostEqual(ptown.y, p.point.y, prec)
 
     def test09_disjoint(self):
         "Testing the `disjoint` lookup type."
diff --git a/django/contrib/gis/tests/test_gdal_geom.py b/django/contrib/gis/tests/test_gdal_geom.py
index 4f16184139..8959d9121f 100644
--- a/django/contrib/gis/tests/test_gdal_geom.py
+++ b/django/contrib/gis/tests/test_gdal_geom.py
@@ -254,8 +254,8 @@ class OGRGeomTest(unittest.TestCase):
 
     def test09b_srs_transform(self):
         "Testing transform()."
-        orig = OGRGeometry('POINT (-104.609252 38.255001)', 4326)
-        trans = OGRGeometry('POINT(992363.390841912 481455.395105533)', 2774)
+        orig = OGRGeometry('POINT (-104.609 38.255)', 4326)
+        trans = OGRGeometry('POINT (992385.4472045 481455.4944650)', 2774)
 
         # Using an srid, a SpatialReference object, and a CoordTransform object
         # or transformations.
@@ -266,8 +266,9 @@ class OGRGeomTest(unittest.TestCase):
         t3.transform(ct)
 
         for p in (t1, t2, t3):
-            self.assertAlmostEqual(trans.x, p.x, 7)
-            self.assertAlmostEqual(trans.y, p.y, 7)
+            prec = 3
+            self.assertAlmostEqual(trans.x, p.x, prec)
+            self.assertAlmostEqual(trans.y, p.y, prec)
 
     def test10_difference(self):
         "Testing difference()."