Compression anastomosis devices having a plurality of distinct pressure profile zones on the surface of the device. The anastomosis devices may be comprised of a plurality of magnetic connecting members arranged in an annular geometry, e.g., a polygon or circle. The anastomosis device may also be a continuous, non-segmented magnet, or other compression anastomosis device. The compression anastomosis device is deployed into a body lumen, e.g., endoscopically and/or laparoscopically, at a target site. A second compression anastomosis device is placed at an adjacent target site in an adjacent lumen. The compression anastomosis devices are brought together and mate, e.g., magnetically, creating an anastomosis.