A bubble fission model that takes into account energy dissipation during violent collapses of cavitation bubbles is introduced by assuming volume conservation and continuity of the gas pressure during instantaneous breakup, invoking either Rayleigh–Taylor instability or high speed microjet formation. In particular, a modified Rayleigh–Plesset equation is derived for the volumetric motion of the fission fragments in rebound. Results obtained under a pressure signal typical for cavitation bubbles confirm the scaling law of Brennen [C. E. Brennen, “Fission of collapsing cavitation bubbles,” J. Fluid Mech. 472, 153 (2002)] and the observations in experiments.