A compression ring (10, 34, 52, 70, 100) to grip and compress body structure such as diverticulum, hemorrhoids, and tissue adjacent a hole. A resilient ring shaped body (12, 36, 54, 72, 102) defines a compression channel (14, 38, 56, 74, 104), and an elongated axially rigid gripping member (16, 40, 58, 76, 106) extends diametrically across the through-opening. The gripping member (106) can rest on a flange (108) on the opposite side of the through-opening or engage with a second gripping member (42, 60, 78) that extends diametrically across the through-opening from the opposite side of the ring. Or, a flexible cage structure (124) can be disposed in the through-opening.
