We calculate the cross section for s-wave neutralino annihilation to t
hree-body final states below the W+W- and t (t) over bar thresholds. S
uch three-body channels may dominate the annihilation cross section if
the neutralino mass is not too much less than m(t) and m(W) respectiv
ely. Furthermore, because neutrinos produced in these channels are muc
h more energetic than those from the b (b) over bar or tau(+)tau(-) ch
annels, they can dominate the energetic-neutrino fluxes from neutralin
o annihilation in the Sun or Earth far below these thresholds and sign
ificantly enhance the neutrino signal in certain regions of the supers
ymmetric parameter space.