A regression-based inverse technique for groundwater modelling that exploits coupling between flow and solute transport is applied to the Gloucester Landfill site near Ottawa, Canada, where hydraulic head and solute concentration data are available. The worth of this technique is demonstrated by comparing model parameter estimates and covariances obtained by matching only concentration data with those obtained by simultaneously matching head and concentration data. For the simultaneous match to both heads and concentrations, optimal weighting of the head residuals with respect to the concentration residuals was established through an iterative technique to equalize the variances of the two residual populations. Statistical analyses indicate that the parameter estimates obtained by matching both the head and concentration data are more certain than estimates obtained by matching concentration data alone. The significance of this greater certainty is demonstrated by translating parameter uncertainty into concentration prediction uncertainty for both parameter sets. For this field application, the predicted peak values are about twice as uncertain when regression estimates are derived solely from concentration data versus those based on both heads and concentrations.