  We have applied Pade approximants to perturbative QCD calculations of event
shape observables in e+e- --> hadrons. We used the exact O(alpha_s^2)
prediction and the [0/1] Pade approximant to estimate the O(alpha_s^3) term for
15 observables, and in each case determined alpha_s(M_Z^2) from comparison with
hadronic Z^0 decay data from the SLD experiment. We found the scatter among the
alpha_s(M_Z^2) values to be significantly reduced compared with the standard
O(alpha_s^2) determination, implying that the Pade method provides at least a
partial approximation of higher-order perturbative contributions to event shape
observables.
