This paper introduces a technique for hybrid BIST time optimization for testing core-based systems that use test pattern broadcasting for both pseudorandom and deterministic patterns. First we formulate the test time minimization problem for such an architecture. Thereafter we present algorithms for finding an efficient combination of pseudorandom and deterministic test sets under given memory constraints, so that the system testing time can be shortened. We also analyze the significance of the pseudorandom sequence quality for the final results. The results are illustrated and the efficiency of the approach is demonstrated by experimental results.