Speed-accuracy trade-offs strongly influence the rate of reward that can be earned in many decision-making tasks. Previous reports suggest that human participants often adopt suboptimal speed-accuracy trade-offs in single session, two-alternative forced-choice tasks. We investigated whether humans acquired optimal speed-accuracy trade-offs when extensively trained with multiple signal qualities. When performance was characterized in terms of decision time and accuracy, our participants eventually performed nearly optimally in the case of higher signal qualities. Rather than adopting decision criteria that were individually optimal for each signal quality, participants adopted a single threshold that was nearly optimal for most signal qualities. However, setting a single threshold for different coherence conditions resulted in only negligible decrements in the maximum possible reward rate. Finally, we tested two hypotheses regarding the possible sources of suboptimal performance: (1) favoring accuracy over reward rate and (2) misestimating the reward rate due to timing uncertainty. Our findings provide support for both hypotheses, but also for the hypothesis that participants can learn to approach optimality. We find specifically that an accuracy bias dominates early performance, but diminishes greatly with practice. The residual discrepancy between optimal and observed performance can be explained by an adaptive response to uncertainty in time estimation.