Tangibles on interactive tabletops are tracked by the surface they are placed on, and have been shown to benefit the interaction. However, they are tied to the surface. When picked up, they are no longer recognized, and lose any connection to virtual objects shown by the table. We introduce the interaction concept of Off-Surface Tangibles that are tracked by the surface but continue to support meaningful interactions when lifted off the surface. We present a design space for Off-Surface Tangibles, and design considerations when employing them. We populate the design space with prior work and introduce possible interaction designs for further research.