A pipe string (44) is pulled out by a tug boat (30) from a floating structure (12) such as a production vessel, as pipe sections (54, 56) are connected in series on the vessel, to eventually lay the pipe string in a catenary curve from the vessel to the sea floor and then along the sea floor to a distant subsea well head (86). To save time and cost in coupling the pipe sections, lower fatigue resistant pipe couplings, such as non weld-on couplings (120) that include a threaded sleeve (134), are used to connect pipe sections that will lie in a quiescent zone such as on the sea floor (zone Az), and in a zone (Cz) lying along the middle of the catenary curve. Higher fatigue resistant pipe couplings such as weld-on couplings (150) are used along active zones such as top and bottom zones (Dz, Bz) of the catenary curve.