This article presents two self-paced reading experiments which investigate the role of storage costs associated with maintaining incomplete syntactic dependencies in structural ambiguity resolution. We argue that previous work has been equivocal regarding syntactic influences because it has examined ambiguities where there is little or no resource differential between competing alternatives. The candidate structures of the ambiguities explored here incur substantially different storage costs. The results indicate that storage-based biases can be sufficiently powerful to create difficulty for a structural alternative even when it is promoted by nonsyntactic factors. These findings are incorporated into a model of ambiguity resolution in which structural biases operate as independent graded constraints in selecting between structural alternatives.