  We study the constraints that the operator product expansion imposes on large
$N_c$ inspired QCD models for current-current correlators. We focus on the
constraints obtained by going beyond the leading-order parton computation. We
explicitly show that, assumed a given mass spectrum: linear Regge behavior in
$n$ (the principal quantum number) plus corrections in $1/n$, we can obtain the
logarithmic (and constant) behavior in $n$ of the decay constants within a
systematic expansion in $1/n$. Our example shows that it is possible to have
different large $n$ behavior for the vector and pseudo-vector mass spectrum and
yet comply with all the constraints from the operator product expansion.
