Rule composition makes it possible to model an important kind of deviation from the rule independence criterion – cases in which the application of one rule is directly dependent on that of another, carrier rule. In such cases, the only use of the dependent rule is as part of a composite rule incorporating both the dependent and its carrier. Where the definition of a word form involves two carrier rules, it can further happen that the same dependent rule composes with both of them, engendering a pattern of multiple exponence that deviates from the unique sequence criterion. I discuss two cases of this sort of rule dependency: Limbu verb morphology exhibits a pattern in which dependent rules compose with their carrier rules; Sanskrit presents a pattern of the reverse sort, in which a carrier rule composes with its dependent.