An intraluminal device and method includes positioning the intraluminal device, such as a bariatric device, in a lumen that is subject to peristaltic waves, such as the GI tract. The intraluminal device includes a surface defined by a wall having opposite end portions. The surface is configured to generally conform to the shape and size of a portion of the lumen. The end portions are spaced apart along an axis in the direction of peristaltic movement along the lumen. The cover has at least one opening therein between the end portions in order to resist peristaltic waves causing distal migration of the device.
