This invention relates to the design and function of a single-tether compressible valve replacement prosthesis which can be deployed into a beating heart without extracorporeal circulation using a transcatheter delivery system. The design as discussed combats the process of wear on anchoring tethers over time by using a plurality of stent-attached, centering tethers, which are themselves attached to a single anchoring tether, which extends through the ventricle and is anchored to a securing device located on the epicardium.