We address the problem of determining those constraint domains A for which the traditional logic programming semantics and the constraint logic programming semantics CLP(A) coincide. This reduces to a study of non-standard models of Clark's axioms and the notion of solution compactness introduced in the CLP scheme. The results of this study include the proof of the existence of a free product in the class of algebras defined by Clark's axioms, a characterization of when Clark's axioms form a model complete theory, and a limited characterization of those models of Clark's axioms which form solution compact constraint domains.