Within the pattern mining area, skypatterns enable to express a user-preference point of view according to a dominance relation. In this paper, we deal with the introduction of softness in the skypattern mining problem. First, we show how softness can provide convenient patterns that would be missed otherwise. Then, thanks to Constraint Programming, we propose a generic and efficient method to mine skypatterns as well as soft ones. Finally, we show the relevance and the effectiveness of our approach through experiments on UCI benchmarks and a case study in chemoinformatics for discovering toxicophores.