This paper provides two families of flexible and simple galaxy models. Representatives of many of the families possess the important cosmological cusps, with the density behaving like 1/r or 1/r^1.33 or 1/r^1.5 at small radii. The density falls off between 1/r^3 and 1/r^5 at large radii. We provide analytic and anisotropic distribution functions for all the models. Unlike many existing methods, our algorithm can yield tangentially anisotropic velocity dispersions in the outer parts, and so is useful for modeling populations of satellite galaxies and substructure in host galaxy halos. As an application, we demonstrate the degeneracy between mass and anisotropy for the satellite galaxy population of the Milky Way. This can introduce a factor of ~3 uncertainty in the mass of the Milky Way as inferred from the kinematics of the satellite population.

to appear in AJ, extended appendix, typo corrected from the 2nd version (completely rewritten from the 1st version, see also astro-ph/0508419 for some materials split from the 1st version)