Multiverse debugging is an extension of classical debugging methods, particularly adapted to non-deterministic systems. Recently, a language-independent formalization was proposed. Moreover, multiverse debugging is particularly beneficial for specification and design languages, such as UML. However, this method suffers from scalability issues during breakpoint lookup. This problem arises due to the exhaustive exploration performed on the potentially infinite state-space of the system. In this paper, we tackle this problem by introducing Reduced Multiverse Debugging, an extension proposing a way for the user to define reduction policies used during breakpoint lookup. We enrich the formalization of multiverse debugging with a modular breakpoint lookup strategy, which allows the integration of the reduction policy. We validate our approach by implementing a practical UML Statechart debugger in the AnimUML web framework. We show several ways the reduction can be applied, using methods such as predicate abstraction for breakpoint lookup on an infinite state-space, removing irrelevant variables, or creating classes of equivalent values. Moreover, we show the possibility to integrate probabilistic reduction strategies. Relying on hash collisions, these strategies can be iteratively refined to increase precision.