Owing to its relative simplicity and wide range of applications, static slices are specifically proposed for software maintenance and programunderstanding. Unfortunately, in many cases static slices are overly conservative and therefore too large to supply useful information to the software maintainer. Dynamic slicing methods can produce more precise results, but only for one test case. In this paper we introduce the concept of union slices (the union of dynamic slices for many test cases) and suggest using a combination of static and union slices. This way the size of program parts that need to be investigated can be reduced by concentrating on the most important parts first. We performed a series of experiments with our experimental implementation on three medium size C programs. Our initial results suggest that union slices are in most cases far smaller than the static slices, and that the growth rate of union slices (by adding more test cases) significantly declines after several representative executions of the program.