The solution to the problem of determining the forces between two spheres falling in a viscous medium in the regime of Stokes flow is applied to the question of the collision efficiency of falling cloud droplets. The axial components of the motion of the drops are computed by the method of Stimson and Jeffery; perpendicular components, by the method of Hocking (suitably refined). Integration is carried out step by step with different initial separation distances. The computations show that collision efficiences are continuous curves that approach zero as the ratio of droplet sizes approaches zero and that all approach the same finite value as the ratio of droplet sizes approaches one. No cutoff in collision efficiency is shown for small sizes, but a slight decrease occurs when the ratio of droplet sizes is near 0.6. The equations used in solving the axial and perpendicular components of the motion of the drops are given in an appendix. 27 pp. Ref.