A numerical study is presented of the drainage and rupture of the liquid film between two drops whose centres approach each other at constant velocity. The considerations are restricted to the partially-mobile case (in which the drop viscosity is rate-determining) and to small approach velocities. The latter restriction permits a transformation of the governing equations to a single universal form, which is solved with the help of boundary integral theory. As in the constant force case, the numerical results show the formation of a dimple but the final drainage behaviour differs considerably. Finally, the influence of van der Waals forces is investigated and the results are shown to correspond well with a simple model proposed earlier for the effective critical film-rupture thickness.