  Line-of-sight velocity distributions are crucial for unravelling the dynamics
of hot stellar systems. We present a new formalism based on penalized
likelihood for deriving such distributions from kinematical data, and evaluate
the performance of two algorithms that extract N(V) from absorption-line
spectra and from sets of individual velocities. Both algorithms are superior to
existing ones in that the solutions are nearly unbiased even when the data are
so poor that a great deal of smoothing is required. In addition, the
discrete-velocity algorithm is able to remove a known distribution of
measurement errors from the estimate of N(V). The formalism is used to recover
the velocity distribution of stars in five fields near the center of the
globular cluster Omega Centauri.
