Existing belief merging operators take advantage of all the models from the bases, including those contradicting the integrity constraints. In this paper, we show that this is not suited to every merging scenario. We study the case when the bases are "rationalized" with respect to the integrity constraints during the merging process. We define in formal terms several independence conditions for merging operators and show how they interact with the standard IC postulates for belief merging. Especially, we give an independence-based axiomatic characterization of a distance-based operator.