Where a submarine wellhead is coupled to a floating vessel by a riser in the form of a flexible hose, vessel movements subject the riser to excessive strains where the riser is tethered ask to the vessel. In accordance with the invention, these strains are reduced by pivoting the riser tether about a horizontal axis, and optionally also about a vertical axis. Giving the riser tether at least one degree of rotational freedom is surprisingly beneficial in reducing riser strains, and consequently in reducing the probability of premature failure of the riser.