Many reinforcement learning algorithms, particularly those that rely on return estimates for policy improvement, can suffer from poor sample efficiency and training instability due to high-variance return estimates. In this paper we leverage new results from off-policy evaluation; it has recently been shown that well-designed behaviour policies can be used to collect off-policy data for provably lower variance return estimates. This result is surprising as it means collecting data on-policy is not variance optimal. We extend this key insight to the online reinforcement learning setting, where both policy evaluation and improvement are interleaved to learn optimal policies. Off-policy RL has been well studied (e.g., IMPALA), with correct and truncated importance weighted samples for de-biasing and managing variance appropriately. Generally these approaches are concerned with reconciling data collected from multiple workers in parallel, while the policy is updated asynchronously, mismatch between the workers and policy is corrected in a mathematically sound way. Here we consider only one worker - the behaviour policy, which is used to collect data for policy improvement, with provably lower variance return estimates. In our experiments we extend two policy-gradient methods with this regime, demonstrating better sample efficiency and performance over a diverse set of environments.