  We show that static electro-vacuum black hole space-times containing an
asymptotically flat spacelike hypersurface with compact interior and with both
degenerate and non-degenerate components of the event horizon do not exist,
under the supplementary hypothesis that all degenerate components of the event
horizon have charges of the same sign. This extends previous uniqueness
theorems of Simon and Masood-ul-Alam (where only non-degenerate horizons were
allowed) and Heusler (where only degenerate horizons were allowed).
