Weiser's algorithm for computing interprocedural slices has a serious drawback: it generates spurious criteria which are not feasible in the control ow of the program. When these extraneous criteria are used the slice becomes imprecise in that it has statements that are not relevant to the computation. Horwitz, Reps and Binkley solved this problem by devising the System Dependence Graph with an associated algorithm that produced more precise interprocedural slices. We take a "step backward" and show how to generate exactly the interprocedural slicing criteria needed, using the program's cal l graph or a stack. This technique can also be used on a family of program dependence graphs that represent all procedures in a program and are not interconnected by a system dependence graph. Then we show how to use the Horwitz, Reps and Binkley interprocedural slicing algorithm to generate criteria and show that the criteria so generated are equal to those generated by the call-graph/stack technique. Thus we present alternative, equivalent ways to generate precise slicing criteria across procedure boundaries. And nally we show that under certain circumstances, Weiser's technique for slicing across procedures is a bit "too strong," for it always generates sufficient criteria to obtain the entire program as a slice on any criteria.