diff --git a/rest_framework/routers.py b/rest_framework/routers.py
index 4eec70bda..e2fbfa77b 100644
--- a/rest_framework/routers.py
+++ b/rest_framework/routers.py
@@ -83,6 +83,7 @@ class BaseRouter(object):
 
 
 class SimpleRouter(BaseRouter):
+
     routes = [
         # List route.
         Route(
@@ -258,6 +259,13 @@ class SimpleRouter(BaseRouter):
                     trailing_slash=self.trailing_slash
                 )
 
+                # If there is no prefix, the first part of the url is probably
+                #   controlled by project's urls.py and the router is in an app,
+                #   so a slash in the beginning will (A) cause Django to give
+                #   warnings and (B) generate URLS that will require using '//'.
+                if not prefix and regex[:2] == '^/':
+                    regex = '^' + regex[2:]
+
                 view = viewset.as_view(mapping, **route.initkwargs)
                 name = route.name.format(basename=basename)
                 ret.append(url(regex, view, name=name))