Abstract: A two-groove coupling sleeve for swaged attachment to thin wall tubing. The sleeve is a cylindrical body having a pair of spaced apart annular grooves provided in the inner peripheral wall, the dimensions of the innermost groove conforming to certain relationships with respect to tube wall thickness. The width (W) of the innermost groove is related to the wall thickness (T) of the tubing to which it is to be swaged, according to the relationship, W/T is equal to or greater than 2.2 and the width generally increases with increasing tube wall thickness. A groove depth for the innermost groove is specified for providing a predetermined amount of tube wall deflection in the region of the groove. The sharpness of the grooves is also defined to assure proper tensile strength and sealing capability.