How can people communicate successfully while keeping resource costs low in the face of ambiguity? We present a principled theoretical analysis comparing two strategies for disambiguation in communication: (i) pragmatic reasoning, where communicators reason about each other, and (ii) other-initiated repair, where communicators signal and resolve trouble interactively. Using agent-based simulations and computational complexity analyses, we compare the efficiency of these strategies in terms of communicative success, computation cost and interaction cost. We show that agents with a simple repair mechanism can increase efficiency, compared to pragmatic agents, by reducing their computational burden at the cost of longer interactions. We also find that efficiency is highly contingent on the mechanism, highlighting the importance of explicit formalisation and computational rigour.