Orthogonal connectors are used in drawings of many types of network diagrams, especially those representing electrical circuits. One approach for routing such connectors has been to compute an orthogonal visibility graph formed by intersecting vertical and horizontal lines projected from the corners of all obstacles and then use an A* search over this graph. However the search can be slow since many routes are in some sense topologically equivalent. We introduce obstacle-hugging routes which we conjecture provide a canonical representative for a set of topologically equivalent routes. We also introduce a new 1-bend visibility graph that supports computation of these canonical routes. Essentially this contains a node for each obstacle corner and connector endpoint in the diagram and an edge between two nodes iff they can be connected using an orthogonal connector with one bend. We show that the use of a 1-bend visibility graph significantly improves the speed of orthogonal connector routing.