Pure methods and model fields are useful and common specification constructs that can be interpreted by the introduction of axioms in a program verifier’s underlying proof system. Care has to be taken that these axioms do not introduce an inconsistency into the proof system. This paper describes and proves sound an approach that ensures no inconsistencies are introduced. Unlike some previous syntax-based approaches, this approach is based on semantics, which lets it admit some natural but previously problematical specifications. The semantic conditions are discharged by the program verifier using an SMT solver, and the paper describes heuristics that help avoid common problems in finding witnesses with trigger-based SMT solvers. The paper reports on the positive experience with using this approach in Spec# for over a year.