[en] Dark-matter halos grown in cosmological simulations appear to have central Navarro–Frenk–White-like density cusps with mean values of $d\mathrm{l}\mathrm{o}\mathrm{g}\mathrm{\rho <!--\; ??\; -->}/d\mathrm{l}\mathrm{o}\mathrm{g}r\approx <!--\; ???\; -->-<!--\; ???\; -->1$, and some dispersion, which is generally parametrized by the varying index α 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, ϕ₀—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 ϕ₀, Einasto α, or the central logarithmic slope in the Dehnen–Tremaine analytical γ-models. The range in halo parameters reflects a substantial variation in the binding energies per unit mass of dark-matter halos.