  We use the procedure of pinched-weight Finite Energy Sum Rules (pFESR) to
determine the OPE coefficients a_6, ...,a_16 of the flavor ud V-A correlator in
terms of existing hadronic tau decay data. We show by appropriate weight
choices that the error on the dominant d=6 contribution, which is known to be
related to the K -> Pi Pi matrix elements of the electroweak penguin operator
in the chiral limit, may be reduced to below the ~15% level. The values we
obtain for the OPE coefficients with d>8 are shown to naturally account for the
discrepancies between our results for the d=6 and d=8 terms and those of
previous analyses, which were obtained neglecting d>8 contributions.
