The present invention includes a device for engaging surgical tethers used in surgical repair, allowing for near full load application to the tether without failure at the site of restraint in the holding mechanism, with economical construction, compact size, and manageable complexity, without sharp edges that will cut the polymer fibers, and without requiring expensive polishing. The holding mechanisms comprise a tether, an orifice sheath, and a restraint element. The tether forms a bight projecting from the orifice sheath, the direction of projection being opposite to the direction of functional pull on the tether, where the bight is formed from a continuous tether or from coupled tether ends, and the restraint element is a fusiform structure positioned under the bight of the tether and over an orifice in the orifice sheath.