  Masses of the pseudoscalar $(J^{PC}=0^{-+})$ charmonium and bottomonium
hybrids are determined using QCD Laplace sum-rules. The effects of the
dimension-six gluon condensate are included in our analysis and result in a
stable sum-rule analysis, whereas previous studies of these states were unable
to optimize mass predictions. The pseudoscalar charmonium hybrid is predicted
to have a mass of approximately 3.8 GeV and the corresponding bottomonium
prediction is 10.6 GeV. Calculating the full correlation function, rather than
only the imaginary part, is shown to be necessary for accurate formulation of
the sum-rules. The charmonium hybrid mass prediction is discussed within the
context of the X Y Z resonances.
