Deep submicron technology calls for new design techniques, in which wire and gate delays are accounted to have equal or nearly equal effect on circuit behaviour. Asynchronous speed-independent (SI) circuits, whose behaviour is only robust to gate delay variations, may be too optimistic. On the other hand, building circuits totally delay-insensitive (DI), for both gates and wires, is impractical. The paper presents an approach for automated synthesis of globally DI and locally SI circuits. It is based on order relaxation, a simple graphical transformation of a circuit's behavioural specification, for which Signal Transition Graph, an interpreted Petri net, is used. The method is successfully tested on a set of benchmarks and a realistic design example. It proves effective showing average cost of DI interfacing at about 40% for area and 20% for speed.