  The new BES measurement on the two-body decays of J/psi and psi' into an
axial-vector meson and a pseudoscalar meson is analyzed with the axial-K mixing
including the one-photon annihilation contribution. A somewhat puzzling pattern
of the K_1^+ K^- decay channels can be understood with no tight constraint on
the mixing angle. The branching fractions of the K_1^0 K-bar^0 channels will be
the cleanest source of information to determine the mixing angle from the 1^+
0^- decays of J/psi and psi'.
