We construct the higher twist structure functions that describe inclusive
b hadron decays in regions of phase space where the hadronic
decay products carry high energy but have low invariant mass. We show
that, for B meson decays, there are four new non-vanishing
matrix elements of non-local operators. We show that to subleading
twist these decays are parametrized in terms of four functions. We
compute the tree-level matching for a general heavy-to-light current
and apply it to B -> X_s gamma. Using a simple model for these
functions we estimate the subleading twist contributions to this
decay.