Summary: Packings in 3-dimensional space were constructed of hard spheres of two radii, \(r_A > r_B \). Previous studies have shown that a packing density higher than that possible for equal sized spheres (\(\delta^3=\pi / \sqrt{18}\)), can be achieved for much of the range \(0 < r_A/r_B \leq 0.623 \dots\). This paper completes the range such that there is no \(r_A/r_B \leq 0.623 \dots\) for which the packing density cannot exceed that of optimally packed equal spheres.