diff --git a/rest_framework/pagination.py b/rest_framework/pagination.py
index 0255cfc7f..220e27fb2 100644
--- a/rest_framework/pagination.py
+++ b/rest_framework/pagination.py
@@ -568,7 +568,7 @@ class CursorPagination(BasePagination):
     def get_page_size(self, request):
         return self.page_size
 
-    def get_next_link(self):
+    def get_next_cursor(self):
         if not self.has_next:
             return None
 
@@ -613,10 +613,15 @@ class CursorPagination(BasePagination):
                 offset = self.cursor.offset + self.page_size
                 position = self.previous_position
 
-        cursor = Cursor(offset=offset, reverse=False, position=position)
-        return self.encode_cursor(cursor)
+        return Cursor(offset=offset, reverse=False, position=position)
 
-    def get_previous_link(self):
+    def get_next_link(self):
+        cursor = self.get_next_cursor()
+        if not cursor:
+            return None
+        return replace_query_param(self.base_url, self.cursor_query_param, self.encode_cursor(cursor))
+
+    def get_previous_cursor(self):
         if not self.has_previous:
             return None
 
@@ -661,8 +666,13 @@ class CursorPagination(BasePagination):
                 offset = 0
                 position = self.next_position
 
-        cursor = Cursor(offset=offset, reverse=True, position=position)
-        return self.encode_cursor(cursor)
+        return Cursor(offset=offset, reverse=True, position=position)
+
+    def get_previous_link(self):
+        cursor = self.get_previous_cursor()
+        if not cursor:
+            return None
+        return replace_query_param(self.base_url, self.cursor_query_param, self.encode_cursor(cursor))
 
     def get_ordering(self, request, queryset, view):
         """
@@ -747,8 +757,7 @@ class CursorPagination(BasePagination):
             tokens['p'] = cursor.position
 
         querystring = urlparse.urlencode(tokens, doseq=True)
-        encoded = b64encode(querystring.encode('ascii')).decode('ascii')
-        return replace_query_param(self.base_url, self.cursor_query_param, encoded)
+        return b64encode(querystring.encode('ascii')).decode('ascii')
 
     def _get_position_from_instance(self, instance, ordering):
         field_name = ordering[0].lstrip('-')