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Compositional techniques have been proposed for traditional reachability analysis in order to introduce modularity and to control the state explosion problem. While modularity has been achived, state explosion is still a problem. Indeed, this problem may even be exacerbated as a locally minimised subsystem may contain many states and transitions forbidden by its context or environments. This paper presents a method to alleviate this problem effectively by including context constraints in local subsystem minimisation. The global behaviour generated using the method is observationally equivalent to that generated by compositional reachability analysis without the inclusion of context constraints.Context constraints, specified as interface processes, are restrictions imposed by the environment on subsystem behaviour. The minimisation produces a simplified machine that describes the behaviour of the subsystem constrained by its context. This machine can also be used as a substitute for the original subsystem in the subsequent steps of the compositional reachability analysis. Interface processes capturing context constraints can be specified by users or automatically constructd using a simple algorithm. The concepts in the paper are illustrated with a clients/server system.