Interengaging surgical staples (11, 31, 51, 71) are provided that are useful in systems for the surgical correction of defects in cardiac valves and/or supporting weaknesses in abdominal regions. The staples are constructed with at least one ring (21, 41, 61, 81) extending laterally from the upper end of one staple leg (15, 35, 55, 75), which once implanted provides for interengagement with the next staple by passage of the other leg (13, 33, 53, 73) of it therethrough. Either shape-memory staple design or an implantation tool causes the two staple legs to curve respectively toward each other once having penetrated the tissue, thus gathering and constricting the tissue in a region below the surface thereof. Elastic sections (67, 83) may be provided in the crown connectors to allow flex in the plane thereof.