The effect of liquid compressibility on the dynamics of a single, spherical cavitating bubble is studied. While it is known that compressibility damps the amplitude of bubble rebounds, the extent to which this effect is accurately captured by weakly compressible versions of the Rayleigh–Plesset equation is unclear. To clarify this issue, partial differential equations governing conservation of mass, momentum, and energy are numerically solved both inside the bubble and in the surrounding compressible liquid. Radiated pressure waves originating at the unsteady bubble interface are directly captured. Results obtained with Rayleigh–Plesset type equations accounting for compressibility effects, proposed by Keller and Miksis [J. Acoust. Soc. Am. 68, 628–633 (1980)], Gilmore, and Tomita and Shima [Bull. JSME 20, 1453–1460 (1977)], are compared with those resulting from the full model. For strong collapses, the solution of the latter reveals that an important part of the energy concentrated during the collapse is used to generate an outgoing pressure wave. For the examples considered in this research, peak pressures are larger than those predicted by Rayleigh–Plesset type equations, whereas the amplitudes of the rebounds are smaller.