This paper presents: (a) a framework for assessing the significance of inconsistencies which arise in object-oriented design models that describe software systems from multiple perspectives, and (b) the findings of a series of experiments conducted to evaluate it. The framework allows the definition of significance criteria and measures the significance of inconsistencies as beliefs for the satisfiability of these criteria. The experiments conducted to evaluate it indicate that criteria definable in the framework have the power to create elaborate rankings of inconsistencies in models.