We compute near-field radiative transfer between two spheres of unequal radii R 1 and R 2 such that R 2 40R 1. For R 2 = 40R 1 , the smallest gap to which we have been able to compute radiative transfer is d = 0.016R 1. To accomplish these computations, we have had to modify existing methods for computing near-field radiative transfer between two spheres in the following ways: (1) exact calculations of coefficients of vector translation theorem are replaced by approximations valid for the limit d R 1 , and (2) recursion relations for a normalized form of translation coefficients are derived which enable us to replace computations of spherical Bessel and Hankel functions by computations of ratios of spherical Bessel or spherical Hankel functions. The results are then compared with the predictions of the modified proximity approximation.