We evaluate three meson doorway mechanisms for nucleon-antinucleon
annihilation at rest for the first time. Detailed results are presented for the
final state phi pi0 originating from the 3S1 initial state and for the phi rho
channel originating from 1S0. The results presented also include the improved
contributions from two meson doorway states and from the tree diagrams. For all
the channels considered a consistent explanation of large and small OZI
violations emerges.Comment: 18 pages, 2 PostScript figures, will be published in Eur. Phys. J.