The compositional verification approach of Graf & Steffen aims at avoiding state space explosion for individual processes of a concurrent system. It relies on interfaces that express the behavioural constraints imposed on each process by synchronization with the other processes, thus preventing the exploration of states and transitions that would not be reachable in the global state space. Krimm & Mounier, and Cheung & Kramer proposed two techniques to generate such interfaces automatically. In this report, we propose a refined interface generation technique that derives the interface of a process automatically from the examination of (a subset of) concurrent processes. This technique is applicable to formalisms where concurrent processes are composed either using synchronization vectors or process algebra parallel composition operators (including those of CCS, CSP, muCRL, LOTOS, and E-LOTOS). We implemented this approach in the EXP.OPEN 2.0 tool of the CADP toolbox. Several experiments indicate state space reductions by more than two orders of magnitude for the largest processes.