  We construct a new family of models of our Galaxy in which dark matter and
disc stars are both represented by distribution functions that are analytic
functions of the action integrals of motion. The potential that is
self-consistently generated by the dark matter, stars and gas is determined,
and parameters in the distribution functions are adjusted until the model is
compatible with observational constraints on the circular-speed curve, the
vertical density profile of the stellar disc near the Sun, the kinematics of
nearly 200 000 giant stars within 2 kpc of the Sun, and estimates of the
optical depth to microlensing of bulge stars. We find that the data require a
dark halo in which the phase-space density is approximately constant for
actions |J| \lesssim 140 kpc km ^-1. In real space these haloes have core radii
~ 2 kpc.
