We consider here floating-compression tensegrity systems: prestressed spatial trusses, composed by cables and struts, such that struts are never connected to each other. In particular, we focus on single-layer systems: all the nodal positions are assumed to lie on a closed synclastic surface, such as a sphere or an ellipsoid. In this study we perform the form-finding and the structural design of a new tensegrity dome of small size; then we compare it to a conventional truss structure. Theoretically, floating-compression systems are not the best choice for carrying loads, a fact which is confirmed in this study. Nevertheless, our tensegrity design improves previous ones significantly. The structural performances evaluated here provide a reference point for assessing the feasibility of floating-compression systems.