A common thread through previous rule-based characterizations of process interactions (e.g., Kenstowicz and Kisseberth 1977, Joshi and Kiparksy 1979) is that opaque interactions like counterfeeding and counterbleeding can be generated by the simultaneous application of rules to the UR or input structure, while transparency (feeding and bleeding) requires access to output structures via rule ordering. The same distinction between referencing input vs. output structure pervades the computational literature on subregular phonology (and syntax), with nearly all proposed function classes being defined in terms of input and/or output locality (Chandlee 2014, Burness and McMullin 2019, 2020, Hao and Andersson 2019, Graf 2020, Chandlee and Jardine 2021). These function classes have been used to model a wide range of phonological processes, building toward a consensus---or at least a strong implication---that the phonological grammar requires both input-based and output-based computation. What has not been articulated to date is what kind of mechanism modulates between these two types of computation. Following recent work on the formal properties of opaque maps (Baković and Blumenfeld 2017, 2018, 2019, Chandlee et al. 2018), in this talk I use opacity as a case study to propose such a mechanism. In particular, I will demonstrate that input-local functions can be taken as the default, with the option of switching to output-local as needed. This switch to output-local computation does not have to be stipulated, however, but rather is automatically enforced via the operation of function composition (i.e., ordering) provided the window of locality is restricted to the length of the rule’s structural description. The applicability of this proposal to more recently defined types of opacity (i.e., fed counterfeeding, mutual bleeding, and seeding; Kavitskaya and Staroverov 2010, Baković and Blumenfeld 2019) will also be discussed, as well as some implications for phonological learning.