An implant structure for use in pulling two soft body tissue areas closer together in a patient (e.g., two points along or adjacent to the patient's mitral valve annulus) includes at least two tissue anchor structures that are respectively implantable into the two tissue areas. A tether structure links the two tissue anchors and can be shortened and held in that condition by a cinch structure. Bracing structures are used between the anchors and the tether to help keep the longitudinal axes of the anchors transverse to the tether axis even when the tether is under tension. The tether may be sheathed in a cushioning sleeve to help protect adjacent tissue from erosion by the tether.