One of the tasks that is carried out by certain vessels in the offshore industry is that of laying pipelines, either by S-laying or by J-laying. J-laying, in which the pipeline is lowered down an inclined or vertical tower and curves round in a single direction to become approximately horizontal along the seabed, is used primarily for laying pipeline in deep water (that is typically deeper than 1,000 m). Examples of J-laying arrangements are shown in U.S. Pat. No. 6,524,030, U.S. Pat. No. 6,592,297, WO 2006/054891, WO 2005/085692 and U.S. Pat. No. 6,796,742.