A compression jaw assembly unit for a compressing device for compressing tubular metal parts includes a compression jaw carrier (17) and a compression jaw (16), provided at the compression jaw carrier (17), with a compressing surface (18) that is oriented essentially facing away from the compression jaw carrier (17) and is curved transversely to a compression jaw longitudinal direction (LB) in a compression jaw transverse direction (QB). The compression jaw (16) includes a fixed compression jaw segment (22), which is fixed to the compression jaw carrier (17) and provides a compressing surface segment (24), and at least one movable compression jaw segment (26, 28) providing a compressing surface segment (30, 32). The at least one movable compressing surface segment (26, 28) can be moved in a direction of movement (B) in relation to the fixed compressing surface segment (22) against the prestressing action of a prestressing device (42).