We investigate quark-model predictions for three-body annihilation reactions <p(p)over bar> --> K+K- M near threshold, with particular attention to charged kaons and M = psi, omega. The cross section ratios psi/omega is a sensitive test of the dynamical mechanism that governs the transition. Selection rules are found that depend on the quark-line topology. (C) 1997 Elsevier Science B.V.