  This paper introduces new phase-space models of dwarf spheroidal galaxies
(dSphs). The stellar component has an isotropic, lowered isothermal (or King)
distribution function. A physical basis for the isotropization of stellar
velocities is given by tidal stirring, whilst the isothermality of the
distribution function guarantees the observed flatness of the velocity
dispersion profile in the inner parts. Our models reproduce the data on the
half-light radius and line of sight central velocity dispersion of the dSphs.
We show that different dark halo profiles -- whether cored or cusped -- lead to
very similar mass estimates within one particular radius, namely 1.7 half-light
radii. Deviations between mass measures due to different density profiles are
substantially smaller than the uncertainties propagated by the observational
errors. We produce a mass measure for each of the Milky Way dSphs and find that
the two most massive are the most luminous, namely Sagittarius (~ 2.8 x 10^8
solar masses) and Fornax (~ 1.3 x 10^8 solar masses). The least massive of the
Milky Way satellites are Willman 1 (~ 4 x 10^5 solar masses) and Segue 1 (~ 6 x
10^5 solar masses).
