  Estimates of higher-order contributions for perturbative series in QCD, in
view of their asymptotic nature, are delicate, though indispensable for a
reliable error assessment in phenomenological applications. In this work, the
Adler function and the scalar correlator are investigated, and models for Borel
transforms of their perturbative series are constructed, which respect general
constraints from the operator product expansion and the renormalisation group.
As a novel ingredient, the QCD coupling is employed in the so-called
$C$-scheme, which has certain advantages. For the Adler function, previous
results obtained directly in the $\overline{\rm MS}$ scheme are supported.
Corresponding results for the scalar correlation function are new. It turns out
that the substantially larger perturbative corrections for the scalar
correlator in $\overline{\rm MS}$ are dominantly due to this scheme choice, and
can be largely reduced through more appropriate renormalisation schemes, which
are easy to realise in the $C$-scheme.
