Calculations have been made for the surface-wave velocity and the piezoelectric coupling constant in the multilayered system consisting of an Al2O3 film and a piezoelectric ZnO film on a silicon substrate. It was found that the addition of an Al2O3 film to the ZnO-on-Si configuration substantially reduced the surface-wave dispersion over a range of normalized acoustic wave numbers. A specific example considered gives phase-velocity variations of less than 0.8% over a 40% acoustic bandwidth, and less than 0.08% over a 10% acoustic bandwidth.