Traxler, Pickering, and Clifton (1998) found that ambiguous sentences are read faster than their unambiguous counterparts. This so-called "ambiguity advantage" has presented a major challenge to classical theories of human sentence comprehension (parsing) because its most prominent explanation, in the form of the unrestricted race model (URM), assumes that parsing is non-deterministic. Recently, Swets, Desmet, Clifton, and Ferreira (2008) have challenged the URM. They argue that readers "strategically underspecify" the representation of ambiguous sentences to save time, unless disambiguation is required by task demands. When disambiguation is required, however, readers assign sentences full structure--and Swets et al. provide experimental evidence to this end. On the basis of their findings, they argue against the URM and in favor of a model of task-dependent sentence comprehension. We show through simulations that the Swets et al. data do not constitute evidence for task-dependent parsing because they can be explained by the URM. However, we provide decisive evidence from a German self-paced reading study consistent with Swets et al.'s general claim about task-dependent parsing. Specifically, we show that under certain conditions, ambiguous sentences can be read more slowly than their unambiguous counterparts, suggesting that the parser may create several parses, when required. Finally, we present the first quantitative model of task-driven disambiguation that subsumes the URM, and we show that it can explain both Swets et al.'s results and our findings.