Lock sets are commonly used for dynamic analysis of deadlocks. The standard per-thread lock set construction only considers locks acquired in the same thread, but is unaware of locks acquired in another thread. This leads to false positives and false negatives. The underlying issue is that the commonly used notion of a critical section on which the lock set construction relies ignores events from other threads. We give a trace-based characterization of critical sections that drops this restriction. Critical sections are no longer restricted to a single thread and can cover multiple threads. Such forms of critical sections exist, are natural, and correct the standard formulation. We show how to soundly approximate the trace-based characterization via partial order relations. Thus, we obtain an improved lock set construction that can still be efficiently computed and allows us to remove false positives reported by the DIRK deadlock predictor and remove false negatives by extending the SPDOffline deadlock predictor. We integrate various lock set constructions with increased precision in an extension of SPDOffline. Our extensions remain sound (no false positives) but are more complete (fewer false negatives) w.r.t. SPDOffline. For an extensive standard benchmark suite we can also show that the performance is not affected.