By using the phase theory, it is shown that, just as in the case of the vibrational spectrum of an isotopically disordered diatomic chain, several special points (“special energies”) at which the spectral density vanishes exist in the electronic energy spectrum of a disordered diatomic Kronig-Penney model, provided that the difference between the potential strengths is larger than a certain critical value. It is also shown that the distinct valleys appearing in the spectrum calculated by Agacy and Borland exactly correspond to the special energies which are predicted by the theory.