  Utilizing asymptotic Pade-approximant methods, we estimate the three-loop
order MS-bar coefficients of alpha_s^3[\log(\mu^2/m^2_b(\mu)]^k terms [k =
{0,1,2,3}] within the $b \to u\ell^-\bar{\nu}_\ell$ decay rate. Except for the
coefficient of the k = 0 term, all other coefficients may also be obtained via
renormalization-group (RG) methods. The relative errors in asymptotic
Pade-approximant estimates of the k = {1,2,3} terms are found to be 5.1% or
less, thereby providing an estimate of the theoretical uncertainty in the
asymptotic Pade-approximant estimate of the RG-inaccessible k = 0 term. By a
judicious choice in the renormalization scale parameter, we are able to extract
|V_{ub}| from the inclusive decay rate to within 7% theoretical uncertainty.
