Human performance in complex multiple-task environments depends critically on the interplay between cognitive control and cognitive capacity. In this paper we propose a tractable computational model of how cognitive control and capacity influence the speed and accuracy of decisions made in the event-based prospective memory (PM) paradigm, and in doing so test a new quantitative formulation that measures two distinct components of cognitive capacity (gain and focus) that apply generally to choices among two or more options. Consistent with prior work, individuals used proactive control (increased ongoing task thresholds under PM load) and reactive control (inhibited ongoing task accumulation rates to PM items) to support PM performance. Individuals used cognitive gain to increase the amount of resources allocated to the ongoing task under time pressure and PM load. However, when demands exceeded the capacity limit, resources were reallocated (shared) between ongoing task and PM processes. Extending previous work, individuals used cognitive focus to control the quality of processing for the ongoing and PM tasks based on the particular demand and payoff structure of the environment (e.g., higher focus for higher priority tasks; lower focus under high time pressure and with PM load). Our model provides the first detailed quantitative understanding of cognitive gain and focus as they apply to evidence accumulation models, which – along with cognitive control mechanisms – support decision-making in complex multiple-task environments.