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Debugging consumes a considerable amount of time in software engineering. Even though numerous techniques have been introduced for automated debugging, they are hardly used in practice. Reasons are the computational overhead imposed by these techniques and the lack of sufficiently precise explanations. There is a need for tools which undertake the task of narrowing down the most likely fault locations. In this paper, we focus on dynamic program slicing. In particular, we present a technique that reduces the number of statements contained in a dynamic slice. This technique is based on constraint computations and allows for removing statements from slices which are unlikely to be the root cause for an error. First empirical results indicate an average reduction of the number of statements of more than 28% in the resulting slice compared to relevant slicing.