The principle of minimum error entropy estimation as found in the work of Weidemann and Stear is reformulated as a problem of finding optimum locations of probability densities in a given mixture such that the resulting (differential) entropy is minimized. New results concerning the entropy lower bound are derived. Continuity of the entropy and attaining the minimum entropy are proved in the case where the mixture is finite. Some other examples and situations, in particular that of symmetric unimodal densities, are studied in more detail