A steel pipeline (22) extends in a shallow catenary curve between two floating structures (12, 14). The pipeline is connected to each floating structure in a joint (60, 60B) that has a center lying on or very close to the pitch and roll axes (54, 56, 54B, 56B) of the corresponding structure hull. A first structure has a recess (52) extending upward from the bottom of the first structure hull to at least the pitch and roll axes of the hull. The shallow catenary curve pipeline extends at an incline (C) of many degrees to the vertical into the recess, and the pipeline end (30) connects to a pipe connector (70) lying on the pitch and roll axes. The pipe connector preferably allows free relative pivoting of a plurality of degrees about horizontal axes between itself and the first pipe end.