  Cosmological N-body simulations indicate that the spherically-averaged
density profiles of cold dark matter halos are accurately described by Einasto
profiles, where the logarithmic slope is a power-law of adjustable exponent,
\gamma =dln\rho /dlnr ~ r^\alpha $. The pseudo-phase-space density (PPSD)
profiles of CDM halos also show remarkable regularity, and are well
approximated by simple power laws, Q(r)=\rho /\sigma ^3 ~ r^-\chi . We show
that this is expected from dynamical equilibrium considerations, since Jeans'
equations predict that the pseudo-phase-space density profiles of Einasto halos
should resemble power laws over a wide range of radii. For the values of \alpha
typical of CDM halos, the inner Q profiles of equilibrium halos deviate
significantly from a power law only very close to the center, and simulations
of extremely high-resolution would be needed to detect such deviations
unambiguously. We use an ensemble of halos drawn from the Millennium-II
simulation to study which of these two alternatives describe best the mass
profile of CDM halos. Our analysis indicates that at the resolution of the best
available simulations, both Einasto and power-law PPSD profiles (with
adjustable exponents \alpha and \chi, respectively) provide equally acceptable
fits to the simulations. A full account of the structure of CDM halos requires
understanding how the shape parameters that characterize departures from
self-similarity, like \alpha or \chi, are determined by evolutionary history,
environment or initial conditions.
