Rapid differential rotation in completely degenerate white dwarfs is studied using a perturbation method. The perturbation method proceeds by solving exactly a spherical model which includes the spherically symmetric part of the rotational potential. The non-spherical terms are then calculated by a first order perturbation method. The results are compared with those obtained by Ostriker and Bodenheimer using a more complicated but effectively exact iterative method. The graph of central density against mass agrees to within one per cent and the polar radius to within four per cent. The perturbation method may easily be extended to other stars.