Abstract Program slicing is a technique by which statements are deleted from a program in such a way as to preserve a projection of the original program's semantics. It is shown that slicing algorithms based upon traditional defined and referenced variable sets do not preserve a projection of strict semantics with respect to computations which cause errors. Rather, these approaches preserve a projection of the program's semantics which is lazy with respect to errors. A modified version of defined and referenced variable sets is introduced, which provides the freedom to choose the form of semantics to be preserved.