The properties of the body-centered-cubic (bcc) solid phase of hard spheres are challenging to compute because of its lack of mechanical and thermodynamic stability, yet this structure remains of interest for theoretical and practical reasons. Density-functional theory (DFT) studies of the bcc hard-sphere solid, using the most accurate functionals from fundamental measure theory, have yielded results with unphysical behaviors in structural and thermodynamic properties. We recently reported [Warshavsky et al., J. Chem. Phys. 148, 024502 (2018)] a Monte Carlo (MC) simulation study of hard spheres initiated in a bcc structure. We observed that such systems, even under constant-volume and single-occupancy-cell constraints, rapidly evolved into either a crystalline state with the cI16 structure or one of a few amorphous states. With these observations in mind, we revisited the DFT calculations of the bcc hard-sphere system by allowing for a bcc-to-cI16 structural transformation. Specifically, the free energy functional was minimized with respect to a density profile having two scalar parameters: the traditional alpha parameter characterizing the width of the Gaussian density distribution around each lattice site and a geometric parameter characterizing the bcc-to-cI16 structural transition. The numerical solutions were physically reasonable across the entire density range. At all densities above ρ b σ 3 = 1.0, a cI16 structure had lower free energy than the corresponding perfect bcc structure. The degree of lattice distortion from bcc to cI16 increased with density up to the close-packing limit. Finally, the predicted values of the structural and thermodynamic properties were in excellent agreement with those extracted from our previous MC simulations.