A coupling for joining pipe elements in end to end relation, said coupling comprising: a plurality of segments (12, 14) 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) comprising: a pair of projections (28, 30) positioned in spaced apart relation on opposite sides of said one segment (12, 14) 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, the segments (12, 14) having sidewalls (36, 38) from which the projections (28, 30) extend; a back wall extending between said projections (28, 30), said back wall having an arcuate surface facing said central axis, the sidewalls (36, 38) being attached to the back wall, and together the sidewalls (36, 38) and the back wall defining a gasket pocket; 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; and a ring gasket positioned within said central space in said gasket pocket; said arcuate surface of said at least one projection (28, 30) having a first radius of curvature measured from a first center of curvature; said arcuate surface of said back wall having a second radius of curvature measured from a second center of curvature, said second center of curvature being non-coincident with said first center of curvature as measured in a plane perpendicular to said central axis; the offset distance between said first center of curvature and said second center of curvature resulting in the gasket pocket being an eccentrically shaped gasket pocket of varying depth, said distance (62, 62a) being a first value at a first point midway between said ends (56, 58) of said at least one segment (12, 14), and a second value at a second point proximate to at least one of said ends (56, 58) of said at least one segment (12, 14), said first value being less than said second value, said eccentrically shaped gasket pocket controlling a degree of distortion of said ring gasket out of round;said at least one projection (28, 30) having at least one notch therein positioned at an end thereof; wherein said notch has a length from 5% to 30% of the total length of the arcuate surfaces. a plurality of segments (12, 14) 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) comprising: a pair of projections (28, 30) positioned in spaced apart relation on opposite sides of said one segment (12, 14) 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, the segments (12, 14) having sidewalls (36, 38) from which the projections (28, 30) extend; a back wall extending between said projections (28, 30), said back wall having an arcuate surface facing said central axis, the sidewalls (36, 38) being attached to the back wall, and together the sidewalls (36, 38) and the back wall defining a gasket pocket; 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; and a ring gasket positioned within said central space in said gasket pocket; said arcuate surface of said at least one projection (28, 30) having a first radius of curvature measured from a first center of curvature; said arcuate surface of said back wall having a second radius of curvature measured from a second center of curvature, said second center of curvature being non-coincident with said first center of curvature as measured in a plane perpendicular to said central axis; the offset distance between said first center of curvature and said second center of curvature resulting in the gasket pocket being an eccentrically shaped gasket pocket of varying depth, said distance (62, 62a) being a first value at a first point midway between said ends (56, 58) of said at least one segment (12, 14), and a second value at a second point proximate to at least one of said ends (56, 58) of said at least one segment (12, 14), said first value being less than said second value, said eccentrically shaped gasket pocket controlling a degree of distortion of said ring gasket out of round;said at least one projection (28, 30) having at least one notch therein positioned at an end thereof; wherein said notch has a length from 5% to 30% of the total length of the arcuate surfaces.