A method for closing an opening formed in a wall of a body lumen or body tissue can include positioning a splittable carrier tube adjacent to the opening, the carrier tube having a splittable distal end with an outer surface retaining a closure element in a substantially tubular configuration or having an asymmetrically-elongated tubular shape with a trapezoidal longitudinal cross-sectional profile. The method including splitting a distal end of the carrier tube with a splitter and deploying the closure element from the carrier flaps of the carrier tube and over the splitter to allow the closure element to engage at least a portion of the wall of the body lumen or the body tissue and substantially close the opening.