Binary black hole mergers are among the most violent events in the Universe, leading to extreme warping of spacetime and copious emission of gravitational radiation. Even though black holes are the most compact objects they are not necessarily the most efficient emitters of gravitational radiation in binary systems. The final black hole resulting from a binary black hole merger retains a significant fraction of the pre-merger orbital energy and angular momentum. A non-vacuum system can in principle shed more of this energy than a black hole merger of equivalent mass. We study these super-emitters through a toy model that accounts for the possibility that the merger creates a compact object that retains a long-lived time-varying quadrupole moment. This toy model can capture the merger of neutron stars, but it can also be used to consider more exotic compact binaries. We hope that this toy model can serve as a guide to more rigorous numerical investigations into these systems.