  Small number statistics may heavily affect the structure of the broadening
function in integrated spectra of galactic globular cluster centers. As a
consequence, it is a priori unknown how closely line broadening measure- ments
gauge the intrinsic velocity dispersions at the cores of these stel- lar
systems. We have tackled this general problem by means of Monte Carlo
simulations. An examination of the mode and the frequency distribution of the
measured values of the simulations indicates that the low value measured for
the velocity dispersion of M30 (Zaggia etal 1992) is likely a reliable estimate
of the velocity dispersion at the center of this cluster. The same methodology
applied to the case of M15 suggests that the steep inward rise of the velocity
dispersion found by Peterson, Seitzer and Cudworth (1989) is real, although
less pronounced. Large-aperture observa- tions are less sensitive to
statistical fluctuations, but are unable to detect strong variations in the
dispersion wich occur within the aperture itself.
