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Feature models (FMs) are a popular formalism for describing the commonality and variability of software product lines (SPLs) in terms of features. As SPL development increasingly involves numerous large FMs, scalable modular techniques are required to manage their complexity. In this paper, we present a novel slicing technique that produces a projection of an FM, including constraints. The slicing allows SPL practitioners to find semantically meaningful decompositions of FMs and has been integrated into the FAMILIAR language.