Abstract: Resolution of singularities consists in constructing a non-singular model of an algebraic variety. This is done by applying a proper birational map that is a local isomorphism at the smooth points. Often too much information is lost about the original variety if the smooth points are the only ones where the desingularization map is a local isomorphism. In these cases, a desingularization preserving some minimal singularities is necessary. This suggests the question of whether, given a class of singularity types S, it is possible to remove with a birational map all singularities not in S while still having a local isomorphism over the singularities of type S. We will study this problem when S consists of all stable simple normal crossings.