The cochlear microphonic potential (CM) and the compound action potential (CAP) cannot be measured separately but only in combination. In the literature their individual estimates are conventionally recovered by the so-called CM cancellation technique. This method averages the potential obtained in response to rarefaction and condensation clicks under the assumption that changing the polarity of the clicks only affects the CM sign and does not alter the CAP in any way. However, both theory and evidence suggest that these hypotheses can be critical. In addition, recent contributions in the electrocochleography (ECochG) literature suggested that assessing the influence of stimulus polarity on the evoked CAP may constitute an indicator of clinical usefulness which the CM cancellation method cannot supply. In this work we propose a new algorithm to estimate the cochlear potentials evoked from positive clicks, CAP+ and CM+, and those evoked from negative clicks, CAP– and CM–, by processing the same kind and amount of data employed in the CM cancellation method. The application to real data taken from 3 subjects exhibiting quantitatively and qualitatively different ECochG responses at various levels of stimulation intensity is presented. In addition, simulated problems where the true CAP and CM are known are studied to permit a fair assessment of the proposed technique. Results suggest that the new algorithm is potentially able to point out small differences between CAP+ and CAP–. This encourages its further employment on a larger scale.