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Program slices have potential uses in many software engineering applications. Traditional slicing algorithms, however, do not work correctly on programs that contain explicit jump statements. Two similar algorithms were proposed recently to alleviate this problem. Both require the flowgraph and the program dependence graph of the program to be modified. In this paper, we propose an alternative algorithm that leaves these graphs intact and uses a separate graph to store the additional required information. We also show that this algorithm permits an extremely efficient, conservative adaptation for use with programs that contain only “structured” jump statements.