Described are devices and methods for treating degenerative, congestive heart disease and related valvular dysfunction. Percutaneous and minimally invasive surgical tensioning structures offer devices that mitigate changes in the ventricular structure (i.e., remodeling) and deterioration of global left ventricular performance related to tissue damage precipitating from ischemia, acute myocardial infarction (AMI) or other abnormalities. These tensioning structures can be implanted within various major coronary blood-carrying conduit structures (arteries, veins and branching vessels), into or through myocardium, or into engagement with other anatomic structures that impact cardiac output to provide tensile support to the heart muscle wall which resists diastolic filling pressure while simultaneously providing a compressive force to the muscle wall to limit, compensate or provide therapeutic treatment for congestive heart failure and / or to reverse the remodeling that produces an enlarged heart.