diff --git a/tests/postgres_tests/test_array.py b/tests/postgres_tests/test_array.py
index 770d5a1623..88e34f9ce4 100644
--- a/tests/postgres_tests/test_array.py
+++ b/tests/postgres_tests/test_array.py
@@ -18,7 +18,6 @@ from .models import (
 )
 
 
-@unittest.skipUnless(connection.vendor == 'postgresql', 'PostgreSQL required')
 class TestSaveLoad(TestCase):
 
     def test_integer(self):
@@ -94,7 +93,6 @@ class TestSaveLoad(TestCase):
         self.assertEqual(instance.decimals, loaded.decimals)
 
 
-@unittest.skipUnless(connection.vendor == 'postgresql', 'PostgreSQL required')
 class TestQuerying(TestCase):
 
     def setUp(self):
@@ -274,7 +272,6 @@ class TestMigrations(TransactionTestCase):
         name, path, args, kwargs = field.deconstruct()
         self.assertEqual(path, 'postgres_tests.models.ArrayFieldSubclass')
 
-    @unittest.skipUnless(connection.vendor == 'postgresql', 'PostgreSQL required')
     @override_settings(MIGRATION_MODULES={
         "postgres_tests": "postgres_tests.array_default_migrations",
     })
@@ -291,7 +288,6 @@ class TestMigrations(TransactionTestCase):
             self.assertNotIn(table_name, connection.introspection.table_names(cursor))
 
 
-@unittest.skipUnless(connection.vendor == 'postgresql', 'PostgreSQL required')
 class TestSerialization(TestCase):
     test_data = '[{"fields": {"field": "[\\"1\\", \\"2\\"]"}, "model": "postgres_tests.integerarraymodel", "pk": null}]'
 
diff --git a/tests/postgres_tests/test_hstore.py b/tests/postgres_tests/test_hstore.py
index ac22f322b5..06544163f8 100644
--- a/tests/postgres_tests/test_hstore.py
+++ b/tests/postgres_tests/test_hstore.py
@@ -1,17 +1,14 @@
 import json
-import unittest
 
 from django.contrib.postgres import forms
 from django.contrib.postgres.fields import HStoreField
 from django.contrib.postgres.validators import KeysValidator
 from django.core import exceptions, serializers
-from django.db import connection
 from django.test import TestCase
 
 from .models import HStoreModel
 
 
-@unittest.skipUnless(connection.vendor == 'postgresql', 'PostgreSQL required')
 class SimpleTests(TestCase):
     apps = ['django.contrib.postgres']
 
@@ -36,7 +33,6 @@ class SimpleTests(TestCase):
         self.assertEqual(reloaded.field, value)
 
 
-@unittest.skipUnless(connection.vendor == 'postgresql', 'PostgreSQL required')
 class TestQuerying(TestCase):
 
     def setUp(self):
@@ -115,7 +111,6 @@ class TestQuerying(TestCase):
         )
 
 
-@unittest.skipUnless(connection.vendor == 'postgresql', 'PostgreSQL required')
 class TestSerialization(TestCase):
     test_data = '[{"fields": {"field": "{\\"a\\": \\"b\\"}"}, "model": "postgres_tests.hstoremodel", "pk": null}]'
 
diff --git a/tests/postgres_tests/test_ranges.py b/tests/postgres_tests/test_ranges.py
index c26382a15b..71d3301756 100644
--- a/tests/postgres_tests/test_ranges.py
+++ b/tests/postgres_tests/test_ranges.py
@@ -18,8 +18,6 @@ from .models import RangesModel
 
 
 def skipUnlessPG92(test):
-    if not connection.vendor == 'postgresql':
-        return unittest.skip('PostgreSQL required')(test)
     PG_VERSION = connection.pg_version
     if PG_VERSION < 90200:
         return unittest.skip('PostgreSQL >= 9.2 required')(test)
diff --git a/tests/postgres_tests/test_unaccent.py b/tests/postgres_tests/test_unaccent.py
index 47ccbda519..ba65155301 100644
--- a/tests/postgres_tests/test_unaccent.py
+++ b/tests/postgres_tests/test_unaccent.py
@@ -1,15 +1,11 @@
 # -*- coding: utf-8 -*-
 from __future__ import unicode_literals
 
-import unittest
-
-from django.db import connection
 from django.test import TestCase, modify_settings
 
 from .models import CharFieldModel, TextFieldModel
 
 
-@unittest.skipUnless(connection.vendor == 'postgresql', 'PostgreSQL required')
 @modify_settings(INSTALLED_APPS={'append': 'django.contrib.postgres'})
 class UnaccentTest(TestCase):
 
diff --git a/tests/runtests.py b/tests/runtests.py
index 054a6ded30..8cabb5ebae 100755
--- a/tests/runtests.py
+++ b/tests/runtests.py
@@ -84,7 +84,7 @@ def get_test_modules():
                     os.path.isfile(f) or
                     not os.path.exists(os.path.join(dirpath, f, '__init__.py'))):
                 continue
-            if not connection.vendor == 'postgresql' and f == 'postgres_tests' or f == 'postgres':
+            if connection.vendor != 'postgresql' and f == 'postgres_tests':
                 continue
             modules.append((modpath, f))
     return modules
@@ -230,6 +230,11 @@ def django_tests(verbosity, interactive, failfast, keepdb, reverse, test_labels,
     state = setup(verbosity, test_labels)
     extra_tests = []
 
+    if test_labels and 'postgres_tests' in test_labels and connection.vendor != 'postgres':
+        if verbosity >= 2:
+            print("Removed postgres_tests from tests as we're not running with PostgreSQL.")
+        test_labels.remove('postgres_tests')
+
     # Run the test suite, including the extra validation tests.
     if not hasattr(settings, 'TEST_RUNNER'):
         settings.TEST_RUNNER = 'django.test.runner.DiscoverRunner'