High-level RCCSD(T) calculations are employed to generate potential energy curves for the (3)Sigma(-) and (3)Pi states of KO+. First, these curves are employed to obtain spectroscopic constants for the two cationic states. Second, the curves are employed together with our previous results on KO, to obtain accurate ionization energies for the KO+ <-- KO processes, for the states involved. We conclude that the first adiabatic ionization energy of KO is 6.98 +/- 0.05 eV, with D-0(KO+) = 1460 +/- 20 cm(-1).