  The treatment of the quark mass plays an important role when it comes to
increasing the precision of the predictions of the heavy quark expansion for
inclusive heavy hadron decays. Various short-distance mass schemes have been
invented to minimize the uncertainties induced by the quark mass, which needs
to be extracted from other, independent observables. We suggest to replace the
quark mass directly by an observable such as e.g. the inverse moments of the
cross section for $e^+ e^- \to $ hadrons. We investigate this alternative
strategy and study its impact on the perturbative series.
