  The QCD-coupling is a necessary input in the computation of many observables,
and the parametric error on input parameters can be a dominant source of
uncertainty. The coupling can be extracted by comparing high order perturbative
computations and lattice evaluated moments of mesonic two-point functions with
heavy quarks, which provide a high energy scale for perturbation theory. The
truncation of the perturbative series is an important systematic uncertainty.
We report on our attempt to study this issue by measuring pseudo-scalar
two-point functions in volumes of $L=2\, \text{fm}$ with twisted-mass Wilson
fermions in the quenched approximation. We use full twist, the non-perturbative
clover term and lattice spacings down to $a=0.015\,\text{fm}$ to tame the
sizable discretization effects. Our preliminary results indicate that either
higher order perturbative corrections or the continuum limit are not under
sufficient control despite our small lattice spacings and quark masses
extending beyond $2\,m_{\text{charm}}$.
