The principal-component method of source localization for the background EEG is generalized to arbitrary spatio-temporal decompositions. It is shown that as long as the spatial patterns of the decomposition span the same signal space as the principal spatial components, the computational process of attempting to localize the sources is the same. Decompositions other than the principal components are shown to be superior for the EEG in that they appear to enable individual sources to be better isolated. An example is given using the common spatial pattern decomposition and using a raw varimax rotation of a subset of the common spatial patterns. The results show that the principal component decomposition is almost ineffective for isolating spike and sharp wave activity in an EEG from a patient with epilepsy, that the common spatial pattern decomposition is significantly better and that the varimax rotation is better yet. That the varimax rotation is best is demonstrated by attempting to locate dipole sources inside the brain which account for the spike and sharp wave activity on the scalp. The question which remains is whether there exists some oblique rotation of the basis vectors of the EEG signal space which is optimal for isolating individual sources.