Abstract: Apparatus is provided for performing a medical procedure on a beating heart. A stabilization element is applied to a segment of the heart in order to reduce motion of the segment. A plurality of suction ports are positioned on the stabilization element so as to form respective seals with the segment of the heart while the stabilization element is applied to the segment. The suction ports apply suction forces to the segment of the heart so as to maintain the segment in contact with the stabilization element. A suction control assembly is coupled to the ports. At least one of the suction ports maintains its seal with the segment of the heart even when another one of the suction ports does not form a seal with the segment of the heart.