  We construct large-N_c motivated approximate chiral SU(3) amplitudes of
next-to-next-to-leading order. The amplitudes are independent of the
renormalization scale. Fitting lattice data with those amplitudes allows for
the extraction of chiral coupling constants with the correct scale dependence.
The differences between approximate and full amplitudes are required to be at
most of the order of N^3LO contributions numerically. Applying the approximate
expressions to recent lattice data for meson decay constants, we determine
several chiral couplings with good precision. In particular, we obtain a value
for F_0, the meson decay constant in the chiral SU(3) limit, that is more
precise than all presently available determinations.
