We investigate the stellar populations of the collapsed-core globular clusters M15 and NGC 6624 by fitting observed surface-brightness and projected velocity-dispersion profiles. Our evolving cluster models were generated by the direct Fokker-Planck method and incorporate realistic stellar mass spectra and energy input from binaries formed by three-body interactions. We adopt an evolved power-law mass function with nonluminous remnants of maximum mass 1.0 M.-1.4 M.. We find that M15 is best fitted by postcollapse evolving models with a mass-function slope of x = 0.9 (where x = 1.35 corresponds to the Salpeter mass function) and a maximum remnant mass of 1.3 M.. Our predicted surface-brightness profiles at times of maximal core expansion in the postcollapse phase reproduce the high-resolution profile recently determined from HST observations by Lauer et al. We can also accommodate a remnant mass of 1.4 M. by adjusting the assumed turnoff/giant mass upward slightly. The corresponding velocity-dispersion profile, which rises steeply near the cluster center, agrees well with the recent observation by Peterson, Seitzer, and Cudworth. The steep gradient and large central value of the velocity-dispersion profile are due to core collapse and mass segregation of the nonluminous remnants. We emphasize that it is not necessary to invoke a massive black hole to explain this observation. The rapidly increasing gravitational acceleration profile of our post-collapse evolving model for M15 is sufficient to account for the observed period decrease of the millisecond pulsar PSR 2127+11A. The surface-brightness profile of NGC 6624 is well fitted by postcollapse evolving models with values of x ranging from 0 to 2 which predict central velocity dispersions ranging from 12 to 5 km s-1, respectively. The postcollapse evolving model with intermediate mass-function slope (x = 0.9) predicts a central velocity dispersion of 8 km s-1. Insufficient velocity data are available to constrain the mass-function slope of this cluster. We discuss our model fits in light of the correlation between mass-function slope and cluster metallicity proposed by McClure et al. For both clusters, the central region (r less than or similar 0.3 pc almost-equal-to 7") is dominated by the heavy, nonluminous remnants; this is an important datum for models of the formation of low-mass X-ray binaries and millisecond pulsars in globular clusters.
