  We set new limits on the mass of the Milky Way, making use of the latest
kinematic information for Galactic satellites and halo objects. In order to
bind these sample objects to the Galaxy, their rest-frame velocities must be
lower than their escape velocities at their estimated distances. This
constraint enables us to show that the mass estimate of the Galaxy is largely
affected by several high-velocity objects (Leo I, Pal 3, Draco, and a few FHB
stars), not by a single object alone (such as Leo I), as has often been the
case in past analyses. We also find that a gravitational potential that gives
rise to a declining rotation curve is insufficient to bind many of our sample
objects to the Galaxy; a possible lower limit on the mass of the Galaxy is
about 2.2 x 10^12 Msolar. To be more quantitative, we adopt a Bayesian
likelihood approach to reproduce the observed distribution of the current
positions and motions of the sample, in a prescribed Galactic potential that
yields a flat rotation curve. This method enables a search for the most likely
total mass of the Galaxy, without undue influence in the final result arising
from the presence or absence of Leo I, provided that both radial velocities and
proper motions are used. The most likely total mass derived from this method is
2.5^+0.5_-1.0 x 10^12 Msolar (including Leo I), and 1.8^+0.4_-0.7 x 10^12
Msolar (excluding Leo I).
