  We analyze the spectral moments of the V-A two-point correlation function.
Using all known short-distance constraints and the most recent experimental
data from tau decays, we determine the lowest spectral moments, trying to
assess the uncertainties associated with the so-called violations of
quark-hadron duality. We have generated a large number of "acceptable" spectral
functions, satisfying all conditions, and have used them to extract the wanted
hadronic parameters through a careful statistical analysis. We obtain accurate
values for the ChPT couplings L10 and C87, and a realistic determination of the
dimension six and eight contributions in the operator product expansion,
O6=(-5.4^{+3.6}_{-1.6})*10^-3 GeV^6 and O8=(-8.9^{+12.6}_{-7.4})*10^-3 GeV^8,
showing that the duality-violation effects have been usually underestimated in
previous literature.
