A number of studies have found evidence for the so-called "ambiguity advantage," that is, faster processing of ambiguous sentences compared with unambiguous counterparts. While a number of proposals regarding the mechanism underlying this phenomenon have been made, the empirical evidence so far is far from unequivocal. It is compatible with several theories, including "strategic underspecification" (Swets et al., 2008), "race models" (Logacev & Vasishth, 2016; Van Gompel et al., 2000), and a more recent "coactivation-based account" (Dillon et al., 2019). While all three classes of theories make matching predictions for the "average time" to complete relative clause (RC) attachment in ambiguous compared with unambiguous sentences, their predictions diverge with regard to the "minimum completion times." The speed-accuracy tradeoff procedure was used to test the predictions of all three classes of theories. According to a hierarchical Bayesian model, the speed-accuracy tradeoff functions (SATFs) for ambiguous RC attachment conditions show an earlier departure from chance performance than in either high or low attachment conditions. The results further indicate increased asymptotic accuracy in the ambiguous condition but no increase in processing rate. Taken together, this pattern of results is compatible with the strategic underspecification model and coactivation-based accounts, but not with race models.