  We present our recent results for the pion elastic form factor [1] obtained
within a local-duality three-point sum rule (a Borel sum rule in the limit of
an infinite Borel parameter). Our analysis includes the O(1) and O(\alpha_s)
contributions and is therefore applicable in a broad range of spacelike
momentum transfers. Our results demonstrate in essentially model-independent
way that the O(1) term, which provides the subleading 1/Q^4 power correction at
asymptotically large momentum transfers, contributes more than half of the pion
form factor in the region Q^2 \le 20 GeV^2. To probe the accuracy of
local-duality sum rules for form factors, we apply precisely the same
procedures to extract the form factor in a quantum-mechanical potential model.
Comparison of the exact form factor known in this model with the result of the
sum-rule calculation gives a probe of the systematic error of the method. In
our example this error is found to be at the level of 10-20%. We expect similar
systematic errors for form factors obtained from local-duality sum rules in
QCD.
