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We calculate the cross section for s-wave neutralino annihilation to three-body final states below the W^+ W^- and t-bar t thresholds. Such three-body channels may dominate the annihilation cross section if the neutralino mass is not too much less than m_t and m_W respectively. Furthermore, because neutrinos produced in these channels are much more energetic than those from the or tau^+ tau^- channels, they can dominate the energetic-neutrino fluxes from neutralino annihilation in the Sun or Earth far below these thresholds and significantly enhance the neutrino signal in certain regions of the supersymmetric parameter space.

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