  We compare the performance of mass estimators for elliptical galaxies that
rely on the directly observable surface brightness and velocity dispersion
profiles, without invoking computationally expensive detailed modeling. These
methods recover the mass at a specific radius where the mass estimate is
expected to be least sensitive to the anisotropy of stellar orbits. One method
(Wolf et al. 2010) uses the total luminosity-weighted velocity dispersion and
evaluates the mass at a 3D half-light radius $r_{1/2}$, i.e., it depends on the
GLOBAL galaxy properties. Another approach (Churazov et al. 2010) estimates the
mass from the velocity dispersion at a radius $R_2$ where the surface
brightness declines as $R^{-2}$, i.e., it depends on the LOCAL properties. We
evaluate the accuracy of the two methods for analytical models, simulated
galaxies and real elliptical galaxies that have already been modeled by the
Schwarzschild's orbit-superposition technique. Both estimators recover an
almost unbiased circular speed estimate with a modest RMS scatter ($\lesssim 10
\%$). Tests on analytical models and simulated galaxies indicate that the local
estimator has a smaller RMS scatter than the global one. We show by examination
of simulated galaxies that the projected velocity dispersion at $R_2$ could
serve as a good proxy for the virial galaxy mass. For simulated galaxies the
total halo mass scales with $\sigma_p(R_2)$ as $M_{vir}
\left[M_{\odot}h^{-1}\right] \approx 6\cdot 10^{12} \left(
\frac{\sigma_p(R_2)}{200\, \rm km\, s^{-1}} \right)^{4}$ with RMS scatter
$\approx 40 \%$.
