The construction of a tomography of neuronal sources is limited by a lack of information. A possible way around this problem is to change the biophysical model that underlies the statement of the inverse problem, i.e., searching for magnitudes that can be better determined from the available data. In this report, we describe a mathematical characterization of the type of currents that are actually able to produce the scalp-recorded EEG. Considering this characterization, we reformulate the bioelectric inverse problem. This approach, called ELECTRA, yields some advantages over the classical formulation in terms of the current density vector: (1) the number of unknowns can be reduced, which is equivalent to increasing the number of independent measurements, (2) the constraints used to reformulate the problem are undeniable since they do not imply any hypothesis about brain function but are instead based on the character of the measurements, and (3) existing experimental evidence suggests that the proposed source model characterizes the type of currents that arise in excitable tissues. We conclude that if the latter fact proves to be true for brain tissues, then no additional information is added to the inverse problem by using a more general source model than the one proposed here. Images obtained using this method for synthetic data, as well as early and middle components of human visual evoked responses to checkerboard stimuli, are presented to illustrate the characteristics of the reconstructed maps and their interpretation. Hum.