Electronic double vacancies with one vacancy in the valence shell and one in the core play a role in several physical processes. Such core-valence double vacancies are theoretically analyzed and related to possible experiments. The corresponding wavefunctions and energies for CO, N-2, and H2CO are computed using propagator and configuration interaction methods. The numerical results are analyzed in some detail and are compared to the corresponding single valence vacancies. The analysis is performed by breaking up the binding energy of the double vacancy into the most relevant components, such as hale-hole repulsion and relaxation contributions. It is shown that the double ionization potential is essentially given by single ionization quantities. In particular, we find a kind of "Koopmans theorem" for those dicationic states with an outer valence hole : the double ionization potential (shifted by the core ionization energy) is approximately given by the valence orbital energy of the core ionized state. As typical for double vacancies we encounter, in addition, an interesting singlet-triplet separation problem. Intensities for the production of the dicationic states by valence ionization out of a core ionized initial state are derived. The extent of valence hole localization in the dicationic states is analyzed by a two-hole population analysis. The analysis can be used to simulate the production of core-valence vacancies via Auger decay.