A means for improving the motion stability of a floating, semi-submerged, or submerged body used in, multi-capture-mode wave energy converters (WECs) having two or more bodies, against wave-induced heave, surge, and pitching forces, while reducing the size, mass and cost of such bodies or bases, thus improving the relative motion and hence capture efficiency of such WECs over a broad spectrum of wave periods and wave heights. Stabilizing counter moments against wave-induced motion are substituted by strategic placement of drag plates or planes entraining seawater mass or water-filled cavities within, or attached to, the bases and/or at least one tensioned seabed-affixed cable. The base or reaction-body stabilizing means is disclosed in a two-body multi-capture-mode, deep-water, surface-deployed, wave-terminator-type WEC to concurrently increase wave energy capture efficiency and reduce the volume, mass, and capital cost of the WEC's stabilized reaction body or base.