  The initial radial density profiles of dark matter halos are laid down by
gravitational collapse in hierarchical structure formation scenarios and are
subject to further compression as baryons cool and settle to the halo centers.
We here describe an explicit implementation of the algorithm, originally
developed by Young, to calculate changes to the density profile as the result
of adiabatic infall in a spherical halo model. Halos with random motion are
more resistant to compression than are those in which random motions are
neglected, which is a key weakness of the simple method widely employed.
Young's algorithm results in density profiles in excellent agreement with those
from N-body simulations. We show how the algorithm may be applied to determine
the original uncompressed halos of real galaxies, a step which must be computed
with care in order to enable a confrontation with theoretical predictions from
theories such as LCDM.
