  A method, known as ``minimal renormalon subtraction'' [Phys. Rev. D 97 (2018)
034503, JHEP 2017 (2017) 62], relates the factorial growth of a perturbative
series (in QCD) to the power~$p$ of a power correction $\Lambda^p/Q^p$.
($\Lambda$ is the QCD scale, $Q$ some hard scale.) Here, the derivation is
simplified and generalized to any~$p$, more than one such correction, and cases
with anomalous dimensions. Strikingly, the well-known factorial growth is seen
to emerge already at low or medium orders, as a consequence of constraints on
the $Q$ dependence from the renormalization group. The effectiveness of the
method is studied with the gluonic energy between a static quark and static
antiquark (the ``static energy''). Truncation uncertainties are found to be
under control after next-to-leading order, despite the small exponent of the
power correction ($p=1$) and associated rapid growth seen in the first four
coefficients of the perturbative series.
