  Dark-matter halos grown in cosmological simulations appear to have central
NFW-like density cusps with mean values of $d\log\rho/d\log r \approx -1$, and
some dispersion, which is generally parametrized by the varying index $\alpha$
in the Einasto density profile fitting function. Non-universality in profile
shapes is also seen in observed galaxy clusters and possibly dwarf galaxies.
Here we show that non-universality, at any given mass scale, is an intrinsic
property of DARKexp, a theoretically derived model for collisionless
self-gravitating systems. We demonstrate that DARKexp - which has only one
shape parameter, $\phi_0$ - fits the dispersion in profile shapes of massive
simulated halos as well as observed clusters very well. DARKexp also allows for
cored dark-matter profiles, such as those found for dwarf spheroidal galaxies.
We provide approximate analytical relations between DARKexp $\phi_0$, Einasto
$\alpha$, or the central logarithmic slope in the Dehnen-Tremaine analytical
$\gamma$-models. The range in halo parameters reflects a substantial variation
in the binding energies per unit mass of dark-matter halos.
