Many theorists argue that deduction is based on the construction of mental models or simulations of descriptions. Individuals tend to reason intuitively from a single mental model, but on occasion they make a deliberate search for alternative models. Previous computer implementations of the theory were deterministic, but evidence from empirical studies suggested that a stochastic algorithm would have greater predictive power. We present such a system for inferences from assertions with single quantifiers, such as, “All the agents are lawyers”. This system implements constraints on the size of model, the sorts of individual it represents, and on the likelihood of a search for alternative models. We show that the system yields quantitative predictions at a fine-grained level, and that they fit the data from two experiments better than previous accounts.