We present an algorithm for local, regularized, policy improvement in reinforcement learning (RL) that allows us to formulate model-based and model-free variants in a single framework. Our algorithm can be interpreted as a natural extension of work on KL-regularized RL and introduces a form of tree search for continuous action spaces. We demonstrate that additional computation spent on model-based policy improvement during learning can improve data efficiency, and confirm that model-based policy improvement during action selection can also be beneficial. Quantitatively, our algorithm improves data efficiency on several continuous control benchmarks (when a model is learned in parallel), and it provides significant improvements in wall-clock time in high-dimensional domains (when a ground truth model is available). The unified framework also helps us to better understand the space of model-based and model-free algorithms. In particular, we demonstrate that some benefits attributed to model-based RL can be obtained without a model, simply by utilizing more computation.