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 behavior. Asynchronous speed-independent (SI) circuits, whose behavior 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 because of the lack of effective synthesis methods. The paper presents a new approach for synthesis of globally DI and locally SI circuits. The method, working in two possible design scenarios, either starts from a behavioral specification called Signal Transition Graph (STG) or from the SI implementation of the STG specification. The method locally modifies the initial model in such a way that the resultant behavior of the system does not depend on delays in the input wires. This guarantees delay-insensitivity of the system-environment interface. The suggested approach was successfully tested on a set of benchmarks. Experimental results show that DI interfacing is realized with a relatively moderate cost in area and speed (costs about 40% area penalty and 20% speed penalty).