The process of designing a piezometer network for estimating the sample variogram of the hydraulic gradient is used to illustrate one strategy for designing a sampling network which is both appropriate for the estimation of spatial statistics and efficient in terms of the measurement instrument. Constraints which impacted this design can be broken into three categories: (1) constraints discussed by previous authors and related to increasing confidence in the estimate of the sample variogram, (2) new constraints related to the spatial distribution of sample location for the purpose of estimating the sample variogram, and (3) constraints related to the measurement instrument. After assessing a number of sampling strategies, including uniform grids, randomized grids, various geometric patterns, and scaled sampling patterns, an acceptable design for the present application was developed from a scaled sampling pattern which was modified to utilize the instrument more efficiently. In this situation the final design could not have been established except through consideration of both the statistics to be derived from the sampling effort and the instrument used to obtain the measurements.¿ 1997 American Geophysical Union