diff --git a/src/or/circuitbuild.c b/src/or/circuitbuild.c
index 02414c69ad..f9e7981106 100644
--- a/src/or/circuitbuild.c
+++ b/src/or/circuitbuild.c
@@ -1167,6 +1167,8 @@ ap_stream_wants_exit_attention(connection_t *conn)
   if (conn->type == CONN_TYPE_AP &&
       conn->state == AP_CONN_STATE_CIRCUIT_WAIT &&
       !conn->marked_for_close &&
+      !(TO_EDGE_CONN(conn)->want_onehop) && /* ignore one-hop streams */
+      !(TO_EDGE_CONN(conn)->use_begindir) && /* ignore targetted dir fetches */
       !connection_edge_is_rendezvous_stream(TO_EDGE_CONN(conn)) &&
       !circuit_stream_is_being_handled(TO_EDGE_CONN(conn), 0,
                                        MIN_CIRCUITS_HANDLING_STREAM))