  Distribution functions (DFs) for dynamically warm thin stellar disks residing
in arbitrary axisymmetric potentials are presented which approximately
reproduce pre-described surface-density and velocity-dispersion profiles. The
functional form of the DFs is obtained by `warming-up' a model made entirely of
circular orbits. This can be done in various ways giving different functional
forms for the DF. In the best case, the DF reproduces the pre-described
profiles to within a few per cent for a typical case reminiscent to the old
stellar disk in the Milky Way. This match may be improved to about one per cent
or better by a simple iterative method. An algorithm is given to draw
phase-space points randomly from the DFs for the purpose of, e.g., N-body
simulations. All the relevant computer programs are available from the author.
