  We perform a stability analysis of a recently proposed sum rule for pion
Compton scattering at fixed angle and moderate Mandelstam invariants. The sum
rule is found to be sensitive to the parameter $\lambda^2$, the contour radius
of a generalized Borel transform. A modified phenomenological model for the
continuum contribution is proposed to remove this dependence. It is shown that
the best value of the quark-hadron duality interval $s_0=0.6$ GeV$^2$ is close
to that in the form factor case ($s_0=0.7$ GeV$^2$). The application of this
new model to the pion form factor is examined. A comparison of our predictions
with those derived from a modified perturbative calculation including Sudakov
suppression is also briefly considered.
