A new variant of fluid thermodynamic perturbation theory is constructed by building on approximations developed by Andersen, Chandler, and Weeks (WCA), directly using a hard-sphere (HS) reference system rather than indirectly via a soft-repulsive reference system. The resulting HS-WCA theory is more forgiving with respect to the choice of a reference HS diameter than the original WCA theory. For example, a simple analytical Boltzmann factor criteria, which relates the reference HS diameter to the distance at which the repulsive pair-potential is equal to kT, is shown to produce global Lennard-Jones fluid thermodynamic predictions that are essentially identical to those of the original WCA theory (or its self-consistent refinement by Lado).