The non-perturbative decoupling of heavy-quarks has proven to be a powerful tool for precision determinations of the QCD coupling, $\alpha_{\rm s}$. A relevant part of the current error on $\alpha_{\rm s}$, however, comes from the systematic uncertainty related to the limited (low-order, perturbative) knowledge of the ${\rm O}(am)$-improvement coefficient, $b_{\rm g}$. After reviewing the relevance and impact of $b_{\rm g}$ in the decoupling strategy followed by the ALPHA Collaboration, I will present some first results from a novel, practical, way to determine $b_{\rm g}$ non-perturbatively. Time permitting, I will also discuss the implications of these results in reducing the current uncertainty on $\alpha_{\rm s}$.