  We consider the short-distance behaviour of the product of the Noether O(N)
currents in the lattice nonlinear sigma-model. We compare the numerical results
with the predictions of the operator product expansion, using one-loop
perturbative renormalization-group improved Wilson coefficients. We find that,
even on quite small lattices (m a \approx 1/6), the perturbative operator
product expansion describes that data with an error of 5-10% in a large window
2a \ltapprox x \ltapprox m^{-1}. We present a detailed discussion of the
possible systematic errors.
