Fast choices are in some cases associated with greater choice accuracy, in others with less, an observation that has eluded existing theoretical models. We revisit a canonical model of optimal sequential sampling and find that across problems response time is quasiconcave in choice accuracy. In simple problems, decisions are fast and accurate, but while accuracy declines in problem complexity, expected response time is non-monotone. We show that this observation can reconcile conflicting existing evidence on the relationship between speed and choice accuracy. Although our results illustrate the limitations of using expected response time alone to identify problem complexity, we highlight how choice responses to incentive manipulation can be used to reveal problem complexity.