  We present the first direct evaluation of DI = 3/2 K -> pi pi matrix elements
with the aim of determining all the low-energy constants at NLO in the chiral
expansion. Our numerical investigation demonstrates that it is indeed possible
to determine the K -> pi pi matrix elements directly for the masses and momenta
used in the simulation with good precision. In this range however, we find that
the matrix elements do not satisfy the predictions of NLO chiral perturbation
theory. For the chiral extrapolation we therefore use a hybrid procedure which
combines the observed polynomial behaviour in masses and momenta of our lattice
results, with NLO chiral perturbation theory at lower masses. In this way we
find stable results for the quenched matrix elements of the electroweak penguin
operators (<pi pi (I=2)|O_8|K^0>= (0.68 +- 0.09) GeV^3 and <pi pi
(I=2)|O_7|K^0>= (0.12 +- 0.02) GeV^3 in the NDR-MSbar scheme at the scale 2
GeV), but not for the matrix elements of O_4 (for which there are too many
Low-Energy Constants at NLO for a reliable extrapolation). For all three
operators we find that the effect of including the NLO corrections is
significant (typically about 30%). We present a detailed discussion of the
status of the prospects for the reduction of the systematic uncertainties.
