An exact solution of the two‐dimensional free‐space Poisson equation for a discharge geometry is derived. It allows the calculation of electrode profiles starting from any assumed field distribution in the discharge midplane. Analytic expressions are obtained for a new class of profiles, and their properties are illustrated with the example of an XeCl laser discharge. The new profiles provide excellent field uniformity, and they are much more compact than other analytical profiles such as those of Rogowski and Chang.