The view of language as action is well-entrenched in computational theories of discourse, however previous work has not paid particular attention to the fact that agents' resource bounds must affect the way that dialogue proceeds just as it affects agents' behavior in general. This paper presents results on the role of discourse strategies in improving performance on collaborative tasks when agents are resource-limited. The resource limitation addressed here is limits in inferential capacity, and the interaction of discourse strategies with this limitation is explored through a dialogue simulation environment, Design-World, in which inferential capacity can be parameterized. The results reported here demonstrate that discourse strategies that incorporate redundant information can improve the performance of inference-limited agents to the point of logical omniscience.