We combine the fixed-order evaluation of the $bbar{b}$ sum rules with a non-relativistic effective-theory approach. The combined result for the $n$-th moment includes all terms suppressed with respect to the leading-order result by ${cal O}(alpha_s^3)$ and ${cal O}((alpha_s sqrt{n})^l alpha_s^2)$, counting $alpha_s sqrt{n} sim 1$. When compared to experimental data, the moments thus obtained show a remarkable consistency and allow for an analysis in the whole range $1le nlesssim 16$.
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