  We study the effect of dimension 7 and 8 operators on inclusive semileptonic
B decays and the extraction of |Vcb|. Using moments of semileptonic B decay
spectra and information based on the Lowest-Lying State saturation
Approximation (LLSA) we perform a global fit of the nonperturbative parameters
of the heavy quark expansion including for the first time the O(1/mb^{4,5})
contributions. Higher power corrections appear to have a very small effect on
the extraction of |Vcb|, independently of the weight we attribute to the LLSA.
