An offshore platform is supported by three or more vertically elongated floats connected at their lower ends to nominally vertical tension members, such as riser pipes, which allow the platform to remain horizontal during lateral shifting. Each float has from 40-80% of the total displacement defined by a central prismatic volume extending from end-to-end. The remaining displacement is defined by an annular enlargement lying below the trough of the maximum expected wave. The float shape minimises mooring forces on the tension members.