We have applied Pade approximants to perturbative QCD calculations of
event
shape observables in $e^+e^- \to$ 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.