Software models help develop higher quality systems. The declarative language Alloy and its accompanying automatic analyzer embody a method for developing software models. Our focus in this paper is Alloy models of systems where different operations may mutate the system state, e.g., addition of an element to a sorted container. Researchers have previously used two techniques for modeling state and state mutation in Alloy, but these techniques have not been compared to each other. We propose a third technique and evaluate all these three techniques that embody conceptually different modeling approaches. We use four core subjects, which we model using each technique. Our primary goal is to quantitatively evaluate the techniques by considering the runtime for solving the ensuing SAT formulas. We also discuss practical tradeoffs among the techniques.