We present $O(\alpha_s^2)$ QCD corrections to the fully-differential decay
rate of a $b$-quark into inclusive semileptonic charmless final states. Our
calculation provides genuine two-loop QCD corrections, beyond the
Brodsky-Lepage-Mackenzie (BLM) approximation, to any infra-red safe partonic
observable that can be probed in $b \to X_u e \bar \nu$ decays. Kinematic cuts
that closely match those used in experiments can be fully accounted for. To
illustrate these points, we compute the non-BLM corrections to moments of the
hadronic invariant mass and the hadronic energy with cuts on the lepton energy
and the hadronic invariant mass. Our results remove one of the sources of
theoretical uncertainty that affect the extraction of the CKM matrix element
$|V_{ub}|$ from charmless inclusive B-decays.
