Most wire-routing programs utilize a maze-running technique to route one connection at a time. Once routed, a wire cannot be moved even if it is subsequently discovered to interfere with the successful completion of other connections. The order in which the desired connections are presented to the routing algorithm has therefore been thought to be of critical importance. Experimental evidence is presented, however, to show that the performance of a router, when measured in terms of the total of the minimum (or ideal) lengths of the connections successfully completed, is, in fact, independent of the order in which connections are attempted.