Random error propagation is examined to determine cross second and third virial coefficients from binary gas density measurements by both the indirect and direct methods. Determination of the cross second virial coefficient B,, from Bm at a single composition via the indirect method is optimized when y:el = y:e2, where e, and e, are the pure component uncertainties. When all errors are equal, the equimolar mixture is optimum as expected.Corresponding analysis of the cross third virial coefficients, C1,2 and C, , , ,show that the optimum compositions are not (V3, V3) as expected for equal error distribution, but rather (%, 3/4). Equations presented allow determination of the two optimum compositions, when em varies with composition. Minimization of the combined errors in B,,, C, , , , and C,22via mixture measurements at two compositions provides results near (V3, V3), when all errors are equal. Methods for direct measurement of B,, are reexamined. Optimal compositions are found using third virial coefficient correlations.