The general problem of finding satisfying solutions to constraint-based underspecified representations of quantifier scope is NP-complete. Existing frameworks, including Dominance Graphs, Minimal Recursion Semantics, and Hole Semantics, have struggled to balance expressivity and tractability in order to cover real natural language sentences with efficient algorithms. We address this trade-off with a general principle of coherence, which requires that every variable introduced in the domain of discourse must contribute to the overall semantics of the sentence. We show that every underspecified representation meeting this criterion can be efficiently processed, and that our set of representations subsumes all previously identified tractable sets.