  Instanton effects and three-loop perturbative contributions are incorporated
into QCD sum-rule analyses of pseudoscalar ($J^{PC}=0^{-+}$) gluonium. Gaussian
sum-rules are shown to be superior to Laplace sum-rules in optimized
predictions for pseudoscalar gluonium states in the presence of instanton
contributions. The Gaussian sum-rule analysis yields a pseudoscalar mass of
$(2.65\pm 0.33) GeV$ and width bounded by $\Gamma<530 MeV$. The Laplace
sum-rules provide corroborating evidence in support of the $\approx 2.7 GeV$
mass scale.
