diff --git a/rest_framework/permissions.py b/rest_framework/permissions.py
index d1e84e088..ac616e202 100644
--- a/rest_framework/permissions.py
+++ b/rest_framework/permissions.py
@@ -11,7 +11,21 @@ from rest_framework import exceptions
 SAFE_METHODS = ('GET', 'HEAD', 'OPTIONS')
 
 
-class OperandHolder:
+class OperationHolderMixin:
+    def __and__(self, other):
+        return OperandHolder(AND, self, other)
+
+    def __or__(self, other):
+        return OperandHolder(OR, self, other)
+
+    def __rand__(self, other):
+        return OperandHolder(AND, other, self)
+
+    def __ror__(self, other):
+        return OperandHolder(OR, other, self)
+
+
+class OperandHolder(OperationHolderMixin):
     def __init__(self, operator_class, op1_class, op2_class):
         self.operator_class = operator_class
         self.op1_class = op1_class
@@ -59,18 +73,8 @@ class OR:
         )
 
 
-class BasePermissionMetaclass(type):
-    def __and__(cls, other):
-        return OperandHolder(AND, cls, other)
-
-    def __or__(cls, other):
-        return OperandHolder(OR, cls, other)
-
-    def __rand__(cls, other):
-        return OperandHolder(AND, other, cls)
-
-    def __ror__(cls, other):
-        return OperandHolder(OR, other, cls)
+class BasePermissionMetaclass(OperationHolderMixin, type):
+    pass
 
 
 @six.add_metaclass(BasePermissionMetaclass)
diff --git a/tests/test_permissions.py b/tests/test_permissions.py
index 46ca166c2..381ec448c 100644
--- a/tests/test_permissions.py
+++ b/tests/test_permissions.py
@@ -589,3 +589,14 @@ class PermissionsCompositionTests(TestCase):
             permissions.IsAuthenticated
         )
         assert composed_perm().has_permission(request, None) is True
+
+    def test_several_levels_and_precedence(self):
+        request = factory.get('/1', format='json')
+        request.user = self.user
+        composed_perm = (
+            permissions.IsAuthenticated &
+            permissions.IsAuthenticated |
+            permissions.IsAuthenticated &
+            permissions.IsAuthenticated
+        )
+        assert composed_perm().has_permission(request, None) is True