This invention introduces three-dimensional (3D) damper arrangements that are used to suppress dynamic motions of a subsea line like a riser, on which the dampers are installed. Damping surfaces (shapes) are mounted on the line so that their combined drag per line unit length dampens motions in 3 mutually perpendicular directions: axial, in-plane (IP) and out-of-plane (OOP). 3D suppression is provided by integral 3D dampers or by combining IP-OOP dampers like strakes with neighboring axial dampers. Increased line motions suppression is achieved by decoupling, particularly on dampers mounted in regions of high line curvature and/or small effective tension. This invention also presents Short Lazy Wave (SLW) configurations of rigid catenary risers, which are also used to suppress dynamic motions. 3D dampers can be used together with SLWs. Motion suppression is introduced to reduce dynamic stresses and to increase fatigue life of the lines.