The Pleistocene geologic history of the Rio Grande valley in the Hueco basin included a cycle of sediment erosion and re-aggradation, resulting in unconformable stratification of sediment of contrasting compressibility and stress history. Since the 1950s large groundwater withdrawals have resulted in significant water-level declines and associated land subsidence. Knowledge of the magnitude and variation of specific storage is needed for developing predictive models of subsidence and groundwater flow simulations. Analyses of piezometric and extensometric data in the form of stress-strain diagrams from a 16 month period yield in situ measurements of aquifer-system compressibility across two discrete aquifer intervals. The linear elastic behaviour of the deeper interval indicates over-consolidation of basin deposits, probably resulting from deeper burial depth before the middle Pleistocene. By contrast, the shallow aquifer system displays an inelastic component, suggesting pre-consolidation stress not significantly greater than current effective stress levels for a sequence of late Pleistocene clay. Harmonic analyses of the piezometric response to earth tides in two water-level piezometers provide an independent estimate of specific storage of aquifer sands.