A high-pressure tube compression fitting/flared fitting for use in combination with a thick-walled tube and a connection body wherein a sleeve is in engagement with a thick-walled tube. The sleeve is generally cylindrically shaped with the exterior thereof coated and then etched. The sleeve includes a first and second sharp inner circumferential biting edges which interengage and bite into and through the exterior of the end portion of the thick-walled tube and into the wall portion of the end portion of the thick-walled tube without narrowing the passageway through the thick-walled tube. The process for making the fitting includes placing an end portion of the thick-walled tube into engagement with a tube engaging surface of a tapered generally cylindrical wall of a guide rod.