Control policies trained using deep reinforcement learning often generate stiff, high-frequency motions in response to unexpected disturbances. To promote more natural and compliant balance recovery strategies, we propose a simple modification to the typical reinforcement learning training process. Our key insight is that stiff responses to perturbations are due to an agent’s incentive to maximize task rewards at all times, even as perturbations are being applied. As an alternative, we introduce an explicit recovery stage where tracking rewards are given irrespective of the motions generated by the control policy. This allows agents a chance to gradually recover from disturbances before attempting to carry out their main tasks. Through an in-depth analysis, we highlight both the compliant nature of the resulting control policies, as well as the benefits that compliance brings to legged locomotion. In our simulation and hardware experiments, the compliant policy achieves more robust, energy-efficient, and safe interactions with the environment.