In this paper we build upon results of Padua and Wolfe who introduce two graph transformations to eliminate anti and output dependences. We first give a unified framework for such transformations. Then, given a loop nest, we aim at determining which statements should be transformed so as to break artificial cycles involving anti or output dependences. The problem of finding the minimum number of statements to be transformed is shown to be NP-complete in the strong sense, and we propose two efficient heuristics.