  The Quantum Chromodynamics (QCD) coupling $\alpha_s$ is a central parameter
in the Standard Model of particle physics. However, it depends on theoretical
conventions related to renormalisation and hence is not an observable quantity.
In order to capture this dependence in a transparent way, a novel definition of
the QCD coupling, denoted by $\hat a$, is introduced, whose running is
explicitly renormalisation scheme invariant. The remaining renormalisation
scheme dependence is related to transformations of the QCD scale $\Lambda$, and
can be parametrised by a single parameter $C$. Hence, we call $\hat a$ the
$C$-scheme coupling. The dependence on $C$ can be exploited to study and
improve perturbative predictions of physical observables. This is demonstrated
for the QCD Adler function and hadronic decays of the $\tau$ lepton.
