Abstract: This invention is a respiratory mask for delivering pressurized gas with a perimeter that can be custom fitted to the contours of a person's face by active and individual adjustment of multiple shape-changing members in the body of the mask. In different embodiments of this invention, the shape-changing members may be located around the perimeter of the mask and individually adjusted by inflation, other pneumatic means, hydraulic means, electric means, or magnetic means. The resulting mask can conform to the contours of an individual's face, even while they sleep, so that there are no places around the mask that fit too tightly (causing irritation, skin marks, and pain) and no places that fit too loosely (causing air leaks).