  The contribution of subleading jet functions to inclusive decay distributions
of $B$ mesons are derived from a systematic two-step matching of QCD current
correlators onto soft collinear and heavy quark effective theory. Focusing on
the tree level matching of QCD onto soft collinear effective theory, the
subleading jet functions are defined to all orders in $\alpha_s(\mu_i)$ (with
$\mu_i^2\sim m_b\Lambda_{\rm QCD}$) and are calculated explicitly at first
order in $\alpha_s(\mu_i)$. We present explicit expressions for the decay rates
of $B\to X_u l \bar\nu$ and the $Q_{7\gamma}-Q_{7\gamma}$ contribution to $B\to
X_s \gamma$, where the subleading jet functions are multiplied by a tree level
hard function and appear in a convolution with the leading order shape
function. Together with the recent two loop calculation of the leading order
hard function for $B\to X_u l \bar\nu$, this paper will allow for a more
precise description of inclusive B decays in the end point region.
