  We provide a family of action-based distribution functions (DFs) for the
double-power law family of densities often used to model galaxies. The DF
itself is a double-power law in combinations of the actions, and reduces to the
known limits in the case of a pure power-law at small and large radii. Our
method enables the velocity anisotropy of the model to be tuned, and so the
anisotropy in the inner and outer parts can be specified for the application in
hand. We provide self-consistent DFs for the Hernquist and Jaffe models - both
with everywhere isotropic velocity dispersions, and with kinematics that
gradually becomes more radially anisotropic on moving outwards. We also carry
out this exercise for a cored dark-matter model. These are tailored to
represent dark haloes and elliptical galaxies respectively with kinematic
properties inferred from simulations or observational data. Finally, we relax a
cored luminous component within a dark matter halo to provide a self-consistent
model of a dwarf spheroidal embedded in dark matter. The DFs provide us with
non-rotating spherical stellar systems, but one of the virtues of working with
actions is the relative ease with which such models can be converted into
axisymmetry and triaxiality.
