The main obstacle in describing inclusive decay spectra in QCD — which, in particular, limits the precision in extrapolating the measured ¯B −→ Xs rate to the full phase space as well as in extracting |Vub| from inclusive measurements of charmless semileptonic decays — is their sensitivity to the non-perturbative momentum distribution of the heavy quark in the meson. We show that, despite this sensitivity, resummed perturbation theory has high predictive power. Conventional Sudakov–resummed perturbation theory describing the decay of an onshell heavy quark yields a divergent expansion. Detailed understanding of this divergence in terms of infrared renormalons has paved the way for making quantitative predictions. In particular, the leading renormalon ambiguity cancels out between the Sudakov factor and the quark pole mass. This cancellation requires renormalon resummation but involves no non-perturbative information. Additional effects due to the Fermi motion of the quark in the meson can be systematically taken into account through power corrections, which are only important near the physical endpoint. This way the moments of the ¯B −→ Xs spectrum with experimentally–accessible cuts — which had been so far just parametrized — were recently computed by perturbative means. At Moriond these predictions were confronted with new data from BaBar.