Many applications of SAT solving can profit from minimal models—a partial variable assignment that is still a witness for satisfiability. Examples include software verification, model checking, and counterexample-guided abstraction refinement. In this paper, we examine how a given model can be minimized for SAT instances that have been obtained by Tseitin encoding of a full propositional logic formula. Our approach uses a SAT solver to efficiently minimize a given model, focusing on only the input variables. Experiments show that some models can be reduced by over 50 percent.