A first-order analytical solution of the inverse problem for aquifer steady flow, presented in paper 1 (Rubin and Dagan, this issue), is applied to the Avra Valley aquifer (Clifton and Neuman, 1982). First, the parameters characterizing the statistical structure of the log-transmissivity Y and water head H fields are estimated by a maximum likelihood procedure. The results for Y are in good agreement with those of (Clifton and Neuman, 1982), in spite of the different methodologies. The incorporation of head measurements is shown to have definite advantages in reducing the estimation variances of Y parameters. Next, the best estimates of Y at various points are obtained by simultaneous conditioning on the measurements of Y and H. It is shown that a substantial reduction in the variance of the conditioned Y is achieved by accounting for H measurements, justifying a posteriori the solution of the inverse problem. Finally, the effective recharge, which is assumed to be uniform, but random, is estimated as part of the process. Although the latter is relatively small for Avra Valley, it might be a parameter of considerable interest in other cases. Further applications of the methodology are suggested.