Attenuation-difference, borehole-radar tomography was used to monitor a series of sodium chloride tracer injection tests conducted within the FSE wellfield at the U.S. Geological Survey Fractured-Rock Hydrology Research Site in Grafton County, New Hampshire, USA. Borehole-radar tomography surveys were conducted by using the sequential-scanning and injection method in three boreholes that form a triangular prism of adjoining tomographic image planes. Attenuation-difference data were inverted by using a weighted damped least-squares (WDLS) inversion method and several different solution simplicity schemes to suppress tomogram artifacts induced by the acquisition geometry, the location and magnitude of the anomaly, and noisy data. Qualitatively, flat tomograms generated by minimizing the norm of the first spatial derivative were most effective at suppressing artifacts. Although artifact suppression measures can be somewhat effective, negative consequences or artifact suppression include (1) reduction in the magnitude of the attenuation differences in the vicinity of the target anomaly and (2) blurring of the anomalies. These effects distort estimates of the location and magnitude of attenuation anomalies. In order to estimate robustly the location and magnitude of attenuation differences, areal constraints were imposed on the WDLS inversions to confine changes in attenuation to regions that are intersected by rays with large attenuation differences and bounded by rays with insignificant attenuation differences. Results from forward modeling support the application of these constraints. The resolution matrix was used to model the effects of acquisition geometry, target anomaly shape, location, and magnitude. For this study, the method of forward modeling indicates that estimates of pixel attenuation are improved by applying areal constraints to the WDLS inversions.