A previous approach in which a perturbation method was used to obtain a solution for the steady-state diffusion to a perfectly sinusoidal surface under limiting conditions has been modified and extended to treat the case where the surface can have any arbitrary profile. A solution for the concentration of the reacting species written in terms of the ratio of the surface amplitude to the diffusion layer thickness as the perturbation parameter has been obtained using the integral transform technique for the boundary value problems resulting at each order. From this, the local current density distribution over the surface has been computed and compared for a perfectly sinusoidal profile and several arbitrary irregular profiles. Analysis of the results indicates that asymmetry and irregularity in the surface morphology have an important influence on the local current distribution by causing the locations of the current maxima and minima to shift from the peak and valley positions respectively. Furthermore, the success of this approach in describing the local current density to a surface with relatively high-frequency features shows that it should be useful for further studies of roughness and for comparison with the fractal approaches to the problem.