Apparatus is provided for use with an implant, the apparatus including a tissue anchor (49, 121, 321, 421), which comprises a distal tissue coupling element (50), which is configured to penetrate cardiac tissue, and a proximal implant-penetrating element (47a, 47b) configured to penetrate the implant (60). The proximal implant-penetrating element (47a, 47b) is shaped so as to define a passage (56) therethrough, which passage (56) has at least two openings that are within 1 mm of a proximal end of the implant-penetrating element (47a, 47b). The apparatus also comprises a cord (54) configured to be removably passed through the passage (56). Other applications of the present invention are also described.