Combinatorial enumeration has a variety of important applications, but there is much evidence indicating that students struggle with solving counting problems. The roots of such difficulty, as well as ways to mitigate such difficulty, have not yet been thoroughly studied. In this paper, one particular aspect of students' counting activity is explored--the use of the problem-solving heuristic of solving smaller, similar problems. Drawing upon student data from clinical interviews in which post-secondary students solved counting problems, four ways in which students successfully utilized this strategy are described. Additionally, three potential pitfalls of the strategy are identified and discussed. Finally, the case is made that the strategy is particularly useful within the area of combinatorics.