The central line-of-sight velocity distribution, or velocity profile (VP), of a stellar system with a massive central black hole has more extended wings than a Gaussian. The importance of these wings is studied for the high spatial resolution absorption-line spectra that are now being obtained with the Hubble Space Telescope (HST). As an example, the central VP is calculated for an isotropic dynamical model for M87 with a 5 x 10(9) M. black hole, for observations through a small circular aperture of diameter D. Conventional techniques for the analysis of galaxy spectra that assume Gaussian VPs strongly underestimate the true velocity dispersion (for D = 0.1'', by more than a factor of 2!). At HST resolution it is thus essential to model VP deviations from a Gaussian. An actual VP shape measurement will strongly constrain any dynamical model, but might be difficult to obtain in practice.