The impedance dispersion of a periodically grooved blocking electrode is calculated exactly under the usual assumptions of simple coupling of surface capacitance to bulk resistivity (i.e. neglecting diffusion). The capacitative dispersion is shown to persist over a surprisingly large frequency range, and increases with surface porosity. However, the effect is found to exist at frequencies which are too high to account for experimental observations in aqueous and solid electrolytes. Furthermore, the assumption of simple coupling between surface impedance and bulk impedance is shown to be unable to account for the resistive part of the dispersion curves commonly observed.