Computational phonology has largely proceeded by analyzing processes in isolation, with more recent work investigating process interaction. Our more thorough understanding of the range of ways in which processes can co-occur and interact raises the question of whether different types of interactions likewise differ in computational complexity. This paper addresses that question through a computational analysis of multiple tone sandhi processes in Changting, a Hakka dialect of Chinese. Tone sandhi is a fitting phenomena to study in this regard, given the overlapping nature of triggers and targets both within and across processes. The analysis indicates that despite the challenges Changting tone sandhi has posed for both rule- and constraint-based theories of phonology, its computational complexity is still quite limited.