A cardiac insert or implant is deployed in a patient's heart so as to reduce ventricular volume, thereby improving cardiac function. The insert or implant may be a compressive device such as a tensile member inserted into the patient's heart, and thereafter operated or deployed to bring opposite walls of a ventricle of the patient's heart into at least approximate contact with one another to thereby constrict and close off a lower portion of that ventricle. The compressive device or tensile member is insertable into the patient heart via a catheter threaded through the patient's vascular system and into the patient's heart.