  The Quantum Chromodynamics (QCD) coupling, $\alpha_s$, is not a physical
observable of the theory since it depends on conventions related to the
renormalization procedure. We introduce a definition of the QCD coupling,
denoted by $\hat\alpha_s$, whose running is explicitly renormalization scheme
invariant. The scheme dependence of the new coupling $\hat\alpha_s$ is
parameterized by a single parameter $C$, related to transformations of the QCD
scale $\Lambda$. It is demonstrated that appropriate choices of $C$ can lead to
substantial improvements in the perturbative prediction of physical
observables. As phenomenological applications, we study $e^+e^-$ scattering and
decays of the $\tau$ lepton into hadrons, both being governed by the QCD Adler
function.
