A coupling for joining pipe elements in end to end relation, said coupling comprising: a plurality of segments (12, 14, 66, 68) joined end to end surrounding a central axis and defining a central space for receiving said pipe elements, at least one of said segments (12, 14, 66, 68) comprising: a pair of projections (28, 30) positioned in spaced apart relation on opposite sides of said one segment and extending toward said central axis, at least a portion of each of said projections (28, 30) being engageable with a respective one of said pipe elements, at least one of said projections (28, 30) having an arcuate surface facing said central axis; a back wall extending between said projections (28, 30), said back wall having an arcuate surface facing said central axis, a distance (62, 62a) between said arcuate surface of said back wall and said arcuate surface of said at least one projection (28, 30), as measured along a radially projecting line extending from said central axis, being a first value at a first point midway between said ends of said at least one segment (12, 14, 66, 68), and a second value at a second point proximate to at least one of said ends of said at least one segment, said first value being less than said second value; a ring gasket positioned within said central space, said ring gasket having an outer circumference having a length greater than the sum of the lengths of said arcuate surfaces of said back walls of said segments (12, 14, 66, 68), said ring gasket supporting said segments (12, 14, 66, 68) in spaced apart relation; characterized in that said arcuate surface of said back wall comprises a first portion (28, 76) having a curved surface, and a second portion (30, 80) having a curved surface, said second portion (30, 80) being positioned proximate to said at least one end of said at least one segment, any point on said second portion (30, 80) being farther from said central axis than any point on said first portion (28, 76). a pair of projections (28, 30) positioned in spaced apart relation on opposite sides of said one segment and extending toward said central axis, at least a portion of each of said projections (28, 30) being engageable with a respective one of said pipe elements, at least one of said projections (28, 30) having an arcuate surface facing said central axis; a back wall extending between said projections (28, 30), said back wall having an arcuate surface facing said central axis, a distance (62, 62a) between said arcuate surface of said back wall and said arcuate surface of said at least one projection (28, 30), as measured along a radially projecting line extending from said central axis, being a first value at a first point midway between said ends of said at least one segment (12, 14, 66, 68), and a second value at a second point proximate to at least one of said ends of said at least one segment, said first value being less than said second value; a ring gasket positioned within said central space, said ring gasket having an outer circumference having a length greater than the sum of the lengths of said arcuate surfaces of said back walls of said segments (12, 14, 66, 68), said ring gasket supporting said segments (12, 14, 66, 68) in spaced apart relation; characterized in that said arcuate surface of said back wall comprises a first portion (28, 76) having a curved surface, and a second portion (30, 80) having a curved surface, said second portion (30, 80) being positioned proximate to said at least one end of said at least one segment, any point on said second portion (30, 80) being farther from said central axis than any point on said first portion (28, 76).