diff --git a/starlette/graphql.py b/starlette/graphql.py
index a2eebebd..d3a64279 100644
--- a/starlette/graphql.py
+++ b/starlette/graphql.py
@@ -15,9 +15,9 @@ try:
     from graphql.error import GraphQLError
 except ImportError:  # pragma: nocover
     graphene = None
-    AsyncioExecutor = None
-    format_graphql_error = None
-    GraphQLError = None
+    AsyncioExecutor = None  # type: ignore
+    format_graphql_error = None  # type: ignore
+    GraphQLError = None  # type: ignore
 
 
 class GraphQLApp:
diff --git a/starlette/routing.py b/starlette/routing.py
index 52ddcdf2..e71b0035 100644
--- a/starlette/routing.py
+++ b/starlette/routing.py
@@ -561,18 +561,20 @@ class Router:
             await partial.handle(scope, receive, send)
             return
 
-        if scope["type"] == "http" and self.redirect_slashes:
-            if not scope["path"].endswith("/"):
-                redirect_scope = dict(scope)
-                redirect_scope["path"] += "/"
+        if scope["type"] == "http" and self.redirect_slashes and scope["path"] != "/":
+            redirect_scope = dict(scope)
+            if scope["path"].endswith("/"):
+                redirect_scope["path"] = redirect_scope["path"].rstrip("/")
+            else:
+                redirect_scope["path"] = redirect_scope["path"] + "/"
 
-                for route in self.routes:
-                    match, child_scope = route.matches(redirect_scope)
-                    if match != Match.NONE:
-                        redirect_url = URL(scope=redirect_scope)
-                        response = RedirectResponse(url=str(redirect_url))
-                        await response(scope, receive, send)
-                        return
+            for route in self.routes:
+                match, child_scope = route.matches(redirect_scope)
+                if match != Match.NONE:
+                    redirect_url = URL(scope=redirect_scope)
+                    response = RedirectResponse(url=str(redirect_url))
+                    await response(scope, receive, send)
+                    return
 
         await self.default(scope, receive, send)
 
diff --git a/tests/test_routing.py b/tests/test_routing.py
index 5347e8b1..e3de089b 100644
--- a/tests/test_routing.py
+++ b/tests/test_routing.py
@@ -117,6 +117,11 @@ def test_router():
     assert response.status_code == 200
     assert response.text == "User fixed me"
 
+    response = client.get("/users/tomchristie/")
+    assert response.status_code == 200
+    assert response.url == "http://testserver/users/tomchristie"
+    assert response.text == "User tomchristie"
+
     response = client.get("/users/nomatch")
     assert response.status_code == 200
     assert response.text == "User nomatch"