This paper argues that in addition to the standardly accepted distinction between arguments and adjuncts with respect to Condition C, it is necessary to distinguish between clausal and non-clausal adjuncts. Although both types of adjuncts are merged cyclically, only r-expressions in clausal adjuncts can corefer with the coindexed pronoun. This is so because they are embedded in the phase, tripartite quantificational and information structure of the sentence more deeply than the r-expressions in non-clausal adjuncts. The availability of coreference depends on the presuppositional status of the clausal adjunct or the element containing it and on whether the r-expression observes the proposed Background Adjunct Coreference Principle. Further, it will be argued that Condition C can see the whole derivation and must be able to wait until the semantic interface of the highest phase in the sentence.