  The tau hadronic width provides a determination of the strong coupling
constant alpha_s at low energies, since it can be related to a weighted
integral of the Adler function in the complex energy plane. Using Operator
Product Expansion, one sees that the sensitivity to alpha_s comes from the
perturbative contribution, which can be obtained by integrating the
perturbative expansion of the Adler function. Two different prescriptions
proposed to perform this integral, called Fixed-Order Perturbation Theory and
Contour-Improved Perturbation Theory (FOPT and CIPT), yield different results
for the strong coupling constant. Recently, models for the Adler function based
on renormalon calculus have been proposed to determine which of the two methods
is the most accurate, by comparing the resulting asymptotic series with the
true value of the integral. We discuss the assumptions of such ansatz and the
determination of their free parameters. We show that variations of this
renormalon ansatz can yield opposite conclusions concerning the comparison of
CIPT versus FOPT, and that such models are not constrained enough to provide a
definite answer on this issue or to be exploited for a high-precision
determination of alpha_s(m_tau^2).
