PowerList theory is well suited to express recursive, data-parallel algorithms. Its abstractness is very high and ensures simple and correct design of parallel programs. We try to reconcile this high level of abstraction with performance by introducing data-distributions into this theory. One advantage of formally introducing distributions is that it allows us to evaluate costs, depending on the number of available processors, which is considered as a parameter. The analysis of the possible distributions for a certain function may also lead to an improvement in the design decisions. Another important advantage is that after the introduction of data-distributions, mappings on real parallel architectures with limited number of processing elements can be analyzed. Case studies for Fast Fourier transform and rank-sorting are given.