Chapter 6 introduces diffusion models with time-varying drift and diffusion rates and decision boundaries, as arise in urgency gating and collapsing boundary models. These models have been proposed for decision making under time pressure, which leads to response time distributions that are more symmetrical than are found otherwise. The chapter critically evaluates the concept of reward-rate optimality as a normative model for how decision makers set their decision criteria and discusses the setting of optimal, time-dependent criteria by solving the Bellman equation. It shows, via the integral equation method, that a model with a linear urgency signal is mathematically equivalent to one with hyperbolic collapsing boundaries and provides explicit response time distribution and accuracy predictions for these models. The chapter reviews empirical evidence for these models and considers other, arguably simpler, mechanisms that may affect performance when decision makers are responding to time pressure, apart from urgency and boundary changes.