A medical apparatus for ligation of tissue and anatomical structures, including fallopian tubes comprises at least two slideable shafts concentrically disposed relative to each other. A first shaft has a tissue receiving recess into which tissue is retracted by a grasper. The grasper is disposed on the end of a second shaft that is extendible from the first shaft. A ring retainer on the second or a third shaft can hold one or more elastic rings that are displaceable by the apparatus around tissue extending from the tissue receiving recess. The rings are held on a tapered or necked down part of the apparatus so that the rings contribute little or nothing to the largest outer diameter (aD) of the portion of the apparatus that is inserted into a patient's body. Because the ring or rings do not contribute to the aD of the apparatus, the apparatus may be constructed to fit within insertion channels of 5mm or less.