Merging efficiently into roundabouts represents a challenge for autonomous vehicles due to the speed difference between merging traffic flows and the lack of certainty regarding drivers' intent, specially when the road is shared with human drivers and/or inter-vehicle communication is not available. We propose herein a strategy to merge into roundabouts, which is based on characterizing the set of merging trajectories that are safe w.r.t. the traffic on the circulatory lane and reachable by the ego vehicle. Our solution leverages the belief that some vehicles in the roundabout will exit the intersection following a non-conflicting path, and generates efficient merging trajectories without compromising safety. Moreover, our decision-making policy is formulated at a high level and does not involve explicitly generating any trajectory, whereby the required computational time remains sufficiently low. In simulation, our strategy brings benefits not only to the smoothness of the merging trajectories themselves but also to the overall traffic performance, which improves 25% w.r.t. a simpler reactive merging approach.