This paper describes a framework for compositional supervisor synthesis, which is applicable to all discrete event systems modeled as a set of deterministic automata. Compositional synthesis exploits the modular structure of the input model, and therefore works best for models consisting of a large number of small automata. The state-space explosion is mitigated by the use of abstraction to simplify individual components, and the property of synthesis equivalence guarantees that the final synthesis result is the same as it would have been for the non-abstracted model. The paper describes synthesis equivalent abstractions and shows their use in an algorithm to efficiently compute supervisors. The algorithm has been implemented in the DES software tool Supremica and successfully computes nonblocking modular supervisors, even for systems with more than 1014 reachable states, in less than 30 seconds.