These proceedings summarize the connection between the factorial growth of coefficients in perturbative QCD and power corrections to the perturbation series, discussed in refs. [1–4]. The improved convergence is shown for three quantities four which four terms in the series are available: the static energy, the quark pole mass, and the polarized Bjorken sum rule. Prospects for determinations of \as\ with controlled truncation uncertainties are discussed, as was found earlier in quark-mass determinations [3, 5].