The Coulomb-gauge QCD Hamiltonian, augmented by a term which produces linear, scalar confinement is used to generate kernels for the bound-state amplitudes and eigenvalues of heavy quarkonium. The model generates all the correct perturbative physics up to order {alpha}{sub {ital s}}{sup 4} and is applied to the {ital c{bar c}} and {ital b{bar b}} systems where good agreement with experiment is obtained.