  We study the twist-3 fragmentation functions $H$ and $\tilde{H}$, by applying
a spectator model. In the calculation we consider the effect of the gluon
rescattering at one loop level. We find that in this case the hard-vertex
diagram, which gives zero contribution to the Collins function, does contribute
to the fragmentation function $H$. The calculation shows that the twist-3 T-odd
fragmentation functions are free of light-cone divergences. The parameters of
the model are fitted from the known parametrization of the unpolarized
fragmentation $D_1$ and the Collins function $H_1^\perp$. We find our result
for the favored fragmentation function is consistent with the recent extraction
on $H$ and $\tilde{H}$ from pp data. We also check numerically the equation of
motion relation for $H$, $\tilde{H}$ and find that relation holds fairly well
in the spectator model.
