We present a combined optical and X-ray analysis of three optically selected X-ray-bright groups with giant elliptical galaxies in the center. These massive ellipticals were targeted for XMM-Newton X-ray observations on the basis of their large-velocity dispersions and their proximity to a nearby ROSAT X-ray source. In addition, these targets are significantly brighter in the optical than their nearest neighbors. We show that one of these systems meets the standard criteria for a fossil group. While the other two systems have a prominent magnitude gap in the E/S0 ridgeline, they do not appear to have reached the fossil-like final stage of group evolution.