This paper studies the use of distortions as a tool for addressing conflicts between a finite number of uncertainty models, in the general case where these initial models may not be precise, in particular a lower probability. We propose to distort the associated credal sets until the global conflict is removed, and to use the conjunction aggregation rule in that moment. We investigate this procedure in the case where the distortion is made using the total variation distance, and compare its properties with other aggregation rules from the literature. In addition, we also explore an alternative where the distortion is tweaked so as to enlarge the credal sets only in the directions where conflict is present.