Plot showing the number of orbits required for a Gaussian clump to phase mix as a function of power-law index for scale-free spherical potentials. The mean position and rotational velocity of the clump is the same as in Figure 1. Different lines correspond to different orbital eccentricities for the clump. We observe that the efficiency of phase mixing is an increasing function of power-law index α, with the Keplerian case as the fastest dispersing. This vindicates the dispersal theorem.