A system for use with a subject, the system comprising: a tether configured to be transluminally advanced into a coronary blood vessel of the heart of the subject, the coronary blood vessel at least partially transcribing a heart chamber of the heart, the tether having a first terminus and a second terminus, the first terminus configured to be advanced through a wall of the coronary blood vessel into the heart chamber at a first location and the second terminus configured to be advanced through the wall of the coronary blood vessel into the heart chamber at a second location; at least one device configured to transluminally draw the first and second termini (10a, 10b) of the tether, from the first and second locations (14a, 14b), respectively, out of the heart chamber, such that a first segment of the tether extends from the first location through the heart chamber and a second segment of the tether extends from the second location through the heart chamber; a support tube defining a lumen, the support tube being configured to be transluminally advanced into the coronary blood vessel, the tether extending through the lumen of the support tube and being slidable relative to the support tube; at least one tissue anchor (50, 56; 80), configured to be slid over and along at least one of the first and second termini (10a, 10b), and to anchor the at least one of the first and second termini (10a, 10b) to tissue of the heart chamber, such that a part of the tether extends between the at least one tissue anchor (50, 56; 80) and the coronary blood vessel; and at least one lock (60, 66; 70), configured, following tensioning of the tether, to lock tension in the tether. a tether configured to be transluminally advanced into a coronary blood vessel of the heart of the subject, the coronary blood vessel at least partially transcribing a heart chamber of the heart, the tether having a first terminus and a second terminus, the first terminus configured to be advanced through a wall of the coronary blood vessel into the heart chamber at a first location and the second terminus configured to be advanced through the wall of the coronary blood vessel into the heart chamber at a second location; at least one device configured to transluminally draw the first and second termini (10a, 10b) of the tether, from the first and second locations (14a, 14b), respectively, out of the heart chamber, such that a first segment of the tether extends from the first location through the heart chamber and a second segment of the tether extends from the second location through the heart chamber; a support tube defining a lumen, the support tube being configured to be transluminally advanced into the coronary blood vessel, the tether extending through the lumen of the support tube and being slidable relative to the support tube; at least one tissue anchor (50, 56; 80), configured to be slid over and along at least one of the first and second termini (10a, 10b), and to anchor the at least one of the first and second termini (10a, 10b) to tissue of the heart chamber, such that a part of the tether extends between the at least one tissue anchor (50, 56; 80) and the coronary blood vessel; and at least one lock (60, 66; 70), configured, following tensioning of the tether, to lock tension in the tether.