The primary application of dimensional analysis (DA) is in problem solving. Typically, the problem description indicates that a physical quantity Y(the unknown) is a function f of other physical quantities A[subscript 1], ..., A[subscript n] (the data). We propose a qualitative problem-solving procedure which consists of a parallel decomposition of the original problem into simple special cases. By simple special cases we mean special cases for which, by DA, the unknown function can be completely determined except for a dimensionless multiplicative constant. The concept of significant special representation of the unknown function is introduced.