Policy-Space Response Oracles (PSRO) is a general algorithmic framework for learning policies in multiagent systems by interleaving empirical game analysis with deep reinforcement learning (DRL). At each iteration, DRL is invoked to train a best response to a mixture of opponent policies. The repeated application of DRL poses an expensive computational burden as we look to apply this algorithm to more complex domains. We introduce two variations of PSRO designed to reduce the amount of simulation required during DRL training. Both algorithms modify how PSRO adds new policies to the empirical game, based on learned responses to a single opponent policy. The first, Mixed-Oracles, transfers knowledge from previous iterations of DRL, requiring training only against the opponent's newest policy. The second, Mixed-Opponents, constructs a pure-strategy opponent by mixing existing strategy's action-value estimates, instead of their policies. Learning against a single policy mitigates conflicting experiences on behalf of a learner facing an unobserved distribution of opponents. We empirically demonstrate that these algorithms substantially reduce the amount of simulation during training required by PSRO, while producing equivalent or better solutions to the game.