A float (1) suitable for use as a buoy or as a component for a wave-powered vehicle. The float (1) includes an upper member (12) whose height can be changed and/or which remained substantially vertical even when the float is in wave-bearing water. A low drag cable (2) suitable for use as a tether in a wave-powered vehicle has a streamlined cross-section and includes a tensile member (21) near the front of the cross-section, at least one non-load-bearing member (22) behind the tensile member, and a polymeric jacket (23). Wave-powered vehicles having a float (1), a submerged swimmer (3) and a tether (2) connecting the float and the swimmer, include a means for determining whether the tether is twisted; or a means (91) for untwisting the tether; or a pressure-sensitive connection (71, 72, 73) which can disconnect the tether when the vehicle is dragged downwards by entanglement with a whale; or a 2-axis universal joint securing the tether to the float or to the swimmer; or elastic elements which absorb snap loads created by the tether; or two or more of these.