  One of the largest theoretical uncertainties assigned to the strong coupling
constant alpha_s as determined from hadronic tau decays stems from the
differences in the results for Fixed Order Perturbation Theory (FOPT), Contour
Improved Perturbation Theory (CIPT) and Renormalon Chain Perturbation Theory
(RCPT). It is often argued that the three methods differ in the treatment of
higher orders only and therefore the full difference should be treated as
theoretical error. Recently other arguments either in favor of FOPT, CIPT or
RCPT have been given, but none of those is able to combine all three to a
single value in the strong coupling constant. In this note I will show that
FOPT alone has a much larger uncertainty than previously assumed and therefore
agrees within error with CIPT. Furthermore a more appropriate matching of the
different schemes used in RCPT reduces the difference to the CIPT result by a
factor of 6. Together with recently published results for the 4th order term
K_4 this reduces the theoretical error on alpha_s by a factor of 2.5 compared
to the previously assumed spread of the three perturbative approaches.
