The primary current distribution at a sinusoidal profile has been solved as a perturbation problem in the amplitude‐to‐wavelength parameter. The results are also applicable to diffusion‐limited reactions on sinusoidal surfaces. The solution for the potential has been developed to the fourth order term. Wagner's solution to this problem can be recovered by including only the first two terms in the perturbation expansion. The expansion technique enables an estimate of the error caused by the neglected terms. The leveling efficiency of a mass‐transfer controlled dissolution reaction is predicted to be always less than that given by Wagner's equation. Applications of the perturbation technique to other relevant problems are discussed.