High-speed observations clearly show that though a collapsing cavitation bubble approaches its minimum size as a coherent single volume, it usually reappears in the first rebounding frame as a cloud of much smaller bubbles or as a highly distorted single volume. This paper explores two mechanisms that may be responsible for that bubble fission process, one invoking a Rayleigh–Taylor stability analysis and the other using the so-called microjet mechanism. Both approaches are shown to lead to qualitatively similar values for the number of fission fragments and the paper investigates the flow parameters that effect that number. Finally, the additional damping of the Rayleigh–Plesset single-bubble calculation caused by the fission process is investigated; it is shown that the fission damping dominates other contributions normally considered and is consistent with the number of collapses and rebounds that are observed to occur in experiments.