A vertical-gradient magnetic system based on optically pumped Cesium sensors has been used to map subtle magnetic anomalies across infilled pit houses and ditches at a medieval archeological site in northern Switzerland. For estimating the locations and dimensions of these features from the recorded data, we have designed and implemented an appropriate inversion scheme. Tests of this scheme on realistic synthetic data sets suggested that suitable minimum magnetic susceptibility contrasts and smoothing parameters for the inversion may be directly extracted from the data. Inversions with minimum magnetic susceptibility contrasts generated causative bodies with maximum plausible sizes. By using higher magnetic susceptibility contrasts, a complete suite of models that matched the data equally well was produced. To constrain better the magnetic susceptibility constrast within a selected area of the archeological site, shallow samples of topsoil and sediment were analyzed in the laboratory. An inversion based on the measured magnetic susceptibility contrast yielded reliable estimates of the locations, 3-D geometries, and sizes of two small pit houses. The depth extent of one pit house was subsequently verified by shallow drilling. We concluded that inversions of vertical-gradient magnetic data constrained by magnetic susceptibility or shallow borehole information are rapid and inexpensive means of providing key knowledge on the depth distribution of inductively magnetized bodies.