Coronal dimmings are closely related to the footpoints of coronal mass ejections (CMEs) and, as such, offer information about CME origins and evolution. In this paper, we investigate the relationship between CME and dimming properties. In particular, we compare CME quantities for events with and without associated dimmings. We find that dimming-associated CMEs, on average, have much higher speeds than non-dimming-associated events. In fact, CMEs without an associated dimming do not appear to travel faster than 800 km s(-1), i.e., the fast solar wind speed. Dimming-associated events are also more likely to be associated with flares, and those flares tend to have the highest magnitudes. We propose that each of these phenomena is affected by the energy available in the source region. Highly energetic source regions produce fast CMEs that are accompanied by larger flares and visible dimmings, while less energetic source regions produce slow CMEs that are accompanied by smaller flares and may or may not have dimmings. The production of dimmings in the latter case may depend on a number of factors including initiation height of the CME, source region magnetic configuration, and observational effects. These results have important implications for understanding and predicting CME initiations.