An apparatus for performing a procedure on a heart valve, the heart valve having an annulus and leaflets, the apparatus comprising: a tissue engaging member including (a) a loop of material configured to contact at least a portion of the annulus or the leaflets when the loop of material is deployed, (b) a plurality of anchors, each of the anchors having a pointy front end, a back end and a slot that runs in a front-to-back direction, wherein the front ends of the anchors are configured for implantation into the annulus or the leaflets in a forward direction, and the anchors are configured so that, subsequent to implantation, the anchors resist extraction from the annulus or the leaflets in a backwards direction, the anchors being arranged with respect to the loop of material so that, when the loop of material is deployed, the anchors are distributed about the loop of material with the front ends of the anchors facing the annulus or the leaflets, and (c) a plurality of linking members that are affixed to the loop of material, at least a portion of each of the linking members passing through the slot in a respective one of the anchors, and each of the linking members being configured to slide with respect to the slot in the respective anchor in the front-to-back direction; and means for implanting the anchors into the annulus or the leaflets so that the tissue engaging member becomes affixed to the annulus or the leaflets. a tissue engaging member including (a) a loop of material configured to contact at least a portion of the annulus or the leaflets when the loop of material is deployed, (b) a plurality of anchors, each of the anchors having a pointy front end, a back end and a slot that runs in a front-to-back direction, wherein the front ends of the anchors are configured for implantation into the annulus or the leaflets in a forward direction, and the anchors are configured so that, subsequent to implantation, the anchors resist extraction from the annulus or the leaflets in a backwards direction, the anchors being arranged with respect to the loop of material so that, when the loop of material is deployed, the anchors are distributed about the loop of material with the front ends of the anchors facing the annulus or the leaflets, and (c) a plurality of linking members that are affixed to the loop of material, at least a portion of each of the linking members passing through the slot in a respective one of the anchors, and each of the linking members being configured to slide with respect to the slot in the respective anchor in the front-to-back direction; and (a) a loop of material configured to contact at least a portion of the annulus or the leaflets when the loop of material is deployed, (b) a plurality of anchors, each of the anchors having a pointy front end, a back end and a slot that runs in a front-to-back direction, wherein the front ends of the anchors are configured for implantation into the annulus or the leaflets in a forward direction, and the anchors are configured so that, subsequent to implantation, the anchors resist extraction from the annulus or the leaflets in a backwards direction, the anchors being arranged with respect to the loop of material so that, when the loop of material is deployed, the anchors are distributed about the loop of material with the front ends of the anchors facing the annulus or the leaflets, and (c) a plurality of linking members that are affixed to the loop of material, at least a portion of each of the linking members passing through the slot in a respective one of the anchors, and each of the linking members being configured to slide with respect to the slot in the respective anchor in the front-to-back direction; and means for implanting the anchors into the annulus or the leaflets so that the tissue engaging member becomes affixed to the annulus or the leaflets.