Two composed interacting services reach a deadlock if their business protocols have behavioral mismatches. A protocol adaptor can resolve deadlocks. However, existing methods build adaptors that process all messages exchanged by the protocols, even if only some messages cause a deadlock. We present an efficient, automated method to construct (if possible) a minimal adaptor for two business protocols containing parallelism and loops. First, the method finds the minimal set of messages exchanged needing adaptation, using behavioral relations on the protocol syntax to identify mismatches. Next, it generates in an efficient way an adaptor from the minimal set of messages. This minimal adaptor is compatible with the protocols, it reduces process...