A pipe coupling for joining pipe elements end-to-end is disclosed. The pipe coupling is formed of segments attached to one another circumferentially straddling the pipe elements. The segments are formed from sub-sections connected to one another end-to-end. Each sub-section has a surface region disposed to engage the outer surfaces of the pipe elements. Each surface region has a different radius of curvature from a surface region on a neighboring sub-section. The radii are selected so that when the coupling segments are deformed around the pipe elements, portions of surface regions of selected sub-sections contact the pipe elements, while portions of surface regions of those sub-sections between the selected portions remain in spaced relation away from the pipe elements. A constant and minimal torque is required to bolt the segments together as a result.