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This paper addresses the problem of automatically inferring synchronization for concurrent programs. Given a program and a specification, we infer synchronization that avoids all interleavings violating the specification, but permits as many valid interleavings as possible. We let the user specify an upper bound on the cost of synchronization, which may limit the observability -- what observations on program state can be made by the synchronization code. We present an algorithm that infers, under certain conditions, the maximally permissive synchronization for a given cost. We implemented a prototype of our approach and applied it to infer synchronization in a number of small programs.