  We utilize asymptotic Pade-approximant methods to estimate the three-loop
order MS bar-scheme coefficients within the inclusive semileptonic b to u decay
rate for four and five active quark flavours. The estimates we obtain for the
three renormalization-group-accessible coefficients within the three-loop
contribution are all found to be within 5.1% of their true values, using a
least-squares procedure in conjunction with an asymptotic Pade-approximant
estimate of the three-loop term over the entire $\mu \ge m_b$ domain. Given the
input values $\alpha_s(M_Z) = 0.118 \pm 0.004$ and $m_b(m_b) =4.17 \pm 0.05
GeV$, the three-loop expression for the purely-perturbative contribution to the
decay rate is minimally sensitive to renormalization scale at $\mu = 1.775
GeV$, at which scale the three-loop contribution is estimated to be only 1.4%
of the leading tree-order contribution. We estimate the full perturbative decay
rate to be $192\pi^3\Gamma(b\to u\bar\nu_\ell\ell^-)/(G_F^2| V_{ub}|^2) = 2070
{\rm GeV^5} \pm 16%$, inclusive of theoretical uncertainties from series
truncation, the input parameters, and the estimation procedure.
