A simple analytical representation of Hartree-Fock atomic densities recently devised defines p(r) as a sum of exponentially decaying functions. This basis set-independent representation is here applied to the calculation of kinetic energies, making use of various well-known kinetic energy functionals. Despite its extreme simplicity, these functions provide highly reliable representations of p(r), allowing the calculation of kinetic energies to within 1% or less. This representation of the density is also analyzed in exchange-only functional calculations. A semiempirical model exchange potential developed before (Pacios, L. F. J. Phys. Chem. 1992, 96, 7294) is here modified and analyzed. This potential presents three valuable features : reproduces the exact exchange energies, exhibits the correct asymptotic trend when r --> infinity, and displays a spatial behavior close to the numerical exchange optimized potential model by Talman et al.