An annuloplasty ring to resize a dilated aortic root during valve sparing surgery includes a scalloped space frame having three trough sections connected to define three crest sections. The annuloplasty ring is mounted outside the aortic root, and extends in height between a base plane and a spaced apart commissure plane of the aortic root. At least two adjacent trough sections are coupled by an annulus-restraining member or tether that limits the maximum deflection of the base of the annuloplasty ring. In use, the tether is preferably located in proximity to the base plane of the aortic root. The annuloplasty ring is movable between a first, substantially conical configuration occurring during a diastolic phase of the cardiac cycle, and a second, substantially cylindrical configuration occurring during a systolic phase of the cardiac cycle.