In Standard Italian, restructuring clauses are characterized by apparently optional transparency effects in the choice of the clausal perfect auxiliary. In the perfect periphrasis, the auxiliary associated with the modal verb can be either HAVE or the one corresponding to the lexical verb (BE or HAVE). In this paper, I argue that there is no true optionality: different auxiliaries show up because the modal verb can select complements of different sizes. Assuming that auxiliary selection is a form of person Agree, different complement sizes determine different Agree domains. In particular, the “transparent” auxiliary results from a vP complement, while a TP complement leads to HAVE insertion.