  We use a recently proposed non-perturbative model, based on an effective
strong coupling constant and free from tunable parameters, to study c-flavoured
hadron production in e+e- annihilation. Charm-quark production is described in
the framework of perturbative fragmentation functions, with NLO coefficient
functions, NLL non-singlet DGLAP evolution and NNLL large-x resummation. We
model hadronization effects by means of the effective coupling constant in the
NNLO approximation and compare our results with experimental data taken at the
Z0 pole and at the Upsilon(4S) resonance. We find that, within the experimental
and theoretical uncertainties, our model is able to give a reasonable
description of D*+-meson spectra from ALEPH for x<1-Lambda/m_c. More serious
discrepancies are instead present when comparing with D and D^* data from BELLE
and CLEO in x-space. Within the errors, our model is nonetheless capable of
reproducing the first ten Mellin moments of all considered data sets. However,
the fairly large theoretical uncertainties call for a full NNLO/NNLL analysis.
