diff --git a/rest_framework/compat.py b/rest_framework/compat.py
index 59217c587..9422e6ad5 100644
--- a/rest_framework/compat.py
+++ b/rest_framework/compat.py
@@ -5,6 +5,8 @@ versions of Django/Python, and compatibility wrappers around optional packages.
 
 from __future__ import unicode_literals
 
+import sys
+
 from django.conf import settings
 from django.core import validators
 from django.utils import six
@@ -34,6 +36,11 @@ try:
 except ImportError:
     ProhibitNullCharactersValidator = None
 
+try:
+    from unittest import mock
+except ImportError:
+    mock = None
+
 
 def get_original_route(urlpattern):
     """
@@ -314,3 +321,7 @@ class MinLengthValidator(CustomValidatorMessage, validators.MinLengthValidator):
 
 class MaxLengthValidator(CustomValidatorMessage, validators.MaxLengthValidator):
     pass
+
+
+# Version Constants.
+PY36 = sys.version_info >= (3, 6)
diff --git a/rest_framework/permissions.py b/rest_framework/permissions.py
index ac616e202..69432d79a 100644
--- a/rest_framework/permissions.py
+++ b/rest_framework/permissions.py
@@ -44,13 +44,13 @@ class AND:
 
     def has_permission(self, request, view):
         return (
-            self.op1.has_permission(request, view) &
+            self.op1.has_permission(request, view) and
             self.op2.has_permission(request, view)
         )
 
     def has_object_permission(self, request, view, obj):
         return (
-            self.op1.has_object_permission(request, view, obj) &
+            self.op1.has_object_permission(request, view, obj) and
             self.op2.has_object_permission(request, view, obj)
         )
 
@@ -62,13 +62,13 @@ class OR:
 
     def has_permission(self, request, view):
         return (
-            self.op1.has_permission(request, view) |
+            self.op1.has_permission(request, view) or
             self.op2.has_permission(request, view)
         )
 
     def has_object_permission(self, request, view, obj):
         return (
-            self.op1.has_object_permission(request, view, obj) |
+            self.op1.has_object_permission(request, view, obj) or
             self.op2.has_object_permission(request, view, obj)
         )
 
diff --git a/tests/test_permissions.py b/tests/test_permissions.py
index 381ec448c..f9d53430f 100644
--- a/tests/test_permissions.py
+++ b/tests/test_permissions.py
@@ -5,6 +5,7 @@ import unittest
 import warnings
 
 import django
+import pytest
 from django.contrib.auth.models import AnonymousUser, Group, Permission, User
 from django.db import models
 from django.test import TestCase
@@ -14,7 +15,7 @@ from rest_framework import (
     HTTP_HEADER_ENCODING, authentication, generics, permissions, serializers,
     status, views
 )
-from rest_framework.compat import is_guardian_installed
+from rest_framework.compat import PY36, is_guardian_installed, mock
 from rest_framework.filters import DjangoObjectPermissionsFilter
 from rest_framework.routers import DefaultRouter
 from rest_framework.test import APIRequestFactory
@@ -600,3 +601,87 @@ class PermissionsCompositionTests(TestCase):
             permissions.IsAuthenticated
         )
         assert composed_perm().has_permission(request, None) is True
+
+    @pytest.mark.skipif(not PY36, reason="assert_called_once() not available")
+    def test_or_lazyness(self):
+        request = factory.get('/1', format='json')
+        request.user = AnonymousUser()
+
+        with mock.patch.object(permissions.AllowAny, 'has_permission', return_value=True) as mock_allow:
+            with mock.patch.object(permissions.IsAuthenticated, 'has_permission', return_value=False) as mock_deny:
+                composed_perm = (permissions.AllowAny | permissions.IsAuthenticated)
+                hasperm = composed_perm().has_permission(request, None)
+                self.assertIs(hasperm, True)
+                mock_allow.assert_called_once()
+                mock_deny.assert_not_called()
+
+        with mock.patch.object(permissions.AllowAny, 'has_permission', return_value=True) as mock_allow:
+            with mock.patch.object(permissions.IsAuthenticated, 'has_permission', return_value=False) as mock_deny:
+                composed_perm = (permissions.IsAuthenticated | permissions.AllowAny)
+                hasperm = composed_perm().has_permission(request, None)
+                self.assertIs(hasperm, True)
+                mock_deny.assert_called_once()
+                mock_allow.assert_called_once()
+
+    @pytest.mark.skipif(not PY36, reason="assert_called_once() not available")
+    def test_object_or_lazyness(self):
+        request = factory.get('/1', format='json')
+        request.user = AnonymousUser()
+
+        with mock.patch.object(permissions.AllowAny, 'has_object_permission', return_value=True) as mock_allow:
+            with mock.patch.object(permissions.IsAuthenticated, 'has_object_permission', return_value=False) as mock_deny:
+                composed_perm = (permissions.AllowAny | permissions.IsAuthenticated)
+                hasperm = composed_perm().has_object_permission(request, None, None)
+                self.assertIs(hasperm, True)
+                mock_allow.assert_called_once()
+                mock_deny.assert_not_called()
+
+        with mock.patch.object(permissions.AllowAny, 'has_object_permission', return_value=True) as mock_allow:
+            with mock.patch.object(permissions.IsAuthenticated, 'has_object_permission', return_value=False) as mock_deny:
+                composed_perm = (permissions.IsAuthenticated | permissions.AllowAny)
+                hasperm = composed_perm().has_object_permission(request, None, None)
+                self.assertIs(hasperm, True)
+                mock_deny.assert_called_once()
+                mock_allow.assert_called_once()
+
+    @pytest.mark.skipif(not PY36, reason="assert_called_once() not available")
+    def test_and_lazyness(self):
+        request = factory.get('/1', format='json')
+        request.user = AnonymousUser()
+
+        with mock.patch.object(permissions.AllowAny, 'has_permission', return_value=True) as mock_allow:
+            with mock.patch.object(permissions.IsAuthenticated, 'has_permission', return_value=False) as mock_deny:
+                composed_perm = (permissions.AllowAny & permissions.IsAuthenticated)
+                hasperm = composed_perm().has_permission(request, None)
+                self.assertIs(hasperm, False)
+                mock_allow.assert_called_once()
+                mock_deny.assert_called_once()
+
+        with mock.patch.object(permissions.AllowAny, 'has_permission', return_value=True) as mock_allow:
+            with mock.patch.object(permissions.IsAuthenticated, 'has_permission', return_value=False) as mock_deny:
+                composed_perm = (permissions.IsAuthenticated & permissions.AllowAny)
+                hasperm = composed_perm().has_permission(request, None)
+                self.assertIs(hasperm, False)
+                mock_allow.assert_not_called()
+                mock_deny.assert_called_once()
+
+    @pytest.mark.skipif(not PY36, reason="assert_called_once() not available")
+    def test_object_and_lazyness(self):
+        request = factory.get('/1', format='json')
+        request.user = AnonymousUser()
+
+        with mock.patch.object(permissions.AllowAny, 'has_object_permission', return_value=True) as mock_allow:
+            with mock.patch.object(permissions.IsAuthenticated, 'has_object_permission', return_value=False) as mock_deny:
+                composed_perm = (permissions.AllowAny & permissions.IsAuthenticated)
+                hasperm = composed_perm().has_object_permission(request, None, None)
+                self.assertIs(hasperm, False)
+                mock_allow.assert_called_once()
+                mock_deny.assert_called_once()
+
+        with mock.patch.object(permissions.AllowAny, 'has_object_permission', return_value=True) as mock_allow:
+            with mock.patch.object(permissions.IsAuthenticated, 'has_object_permission', return_value=False) as mock_deny:
+                composed_perm = (permissions.IsAuthenticated & permissions.AllowAny)
+                hasperm = composed_perm().has_object_permission(request, None, None)
+                self.assertIs(hasperm, False)
+                mock_allow.assert_not_called()
+                mock_deny.assert_called_once()