This paper investigates a hybrid approach to deterministic finite automata (DFA) identification by combining heuristic (EDSM) and exact (reduction to SAT) methods. The hybrid strategy implies first partially identifying the DFA heuristically and then minimizing it with an exact method. Two implementations of the hybrid approach are tested - one using binary search on the number of states of the intermediate model, and one that adjusts the SAT offset to control its search space. The results obtained on datasets from the STAMINA competition show that while the hybrid approach reduces the size of the inferred models compared to EDSM, this does not necessarily translate to better test performance. Nevertheless, the methods used in this work demonstrate how a hybrid approach can be applied to infer more compact models in DFA identification.