A treatment for bioprosthetic tissue used in implants or for assembled bioprosthetic heart valves to reduce in vivo calcification is disclosed. The method includes preconditioning, pre-stressing, or pre-damaging fixed bioprosthetic tissue in a manner that mimics the damage associated with post-implant use, while, and/or subsequently applying a calcification mitigant such as a capping agent or a linking agent to the damaged tissue. The capping agent suppresses the formation of binding sites in the tissue that are exposed or generated by the damage process (service stress) and otherwise would, upon implant, attract calcium, phosphate, immunogenic factors, or other precursors to calcification. The linking agent will act as an elastic reinforcement or shock-absorbing spring element in the tissue structure at the site of damage from the pre-stressing. In one method, tissue leaflets in assembled bioprosthetic heart valves are preconditioned by simulating actual flow conditions for a predetermined number of cycles, during or after which the valve is exposed to the capping agent.