Swets et al. (2008) present evidence that the so-called ambiguity advantage (Traxler et al., 1998), which has been explained in terms of the Unrestricted Race Model, can equally well be explained by assuming underspecification in ambiguous conditions driven by task-demands. Specifically, if comprehension questions require that ambiguities be resolved, the parser tends to make an attachment: when questions are about superficial aspects of the target sentence, readers tend to pursue an underspecification strategy. It is reasonable to assume that individual differences in strategy will play a significant role in the application of such strategies, so that studying average behavior may not be informative. In order to study the predictions of the good-enough processing theory, we implemented two versions of underspecification: the partial specification model (PSM), which is an implementation of the Swets et al. proposal, and a more parsimonious version, the non-specification model (NSM). We evaluate the relative fit of these two kinds of underspecification to Swets et al.’s data; as a baseline, we also fit three models that assume no underspecification. We find that a model without unspecification pro- vides a somewhat better fit than both underspecification models, while the NSM model provides a better fit than the PSM. We interpret the results as lack of unambiguous evidence in favor of underspecification; however, given that there is considerable existing evidence for good-enough processing in the literature, it is reasonable to assume that some underspecification might occur. Under this assumption, the results can be interpreted as tentative ev- idence for NSM over PSM. More generally, our work provides a method for choosing between models of real-time processes in sentence comprehension that make qualitative predictions about the relationship between several de- pendent variables. We believe that sentence processing research will greatly benefit from a wider use of such methods.