Offshore tower structure

An offshore tower structure comprises an upper part 50 having a vertical leg or legs with a uniform horizontal cross section and a lower part having discrete legs 51 arranged in a battered configuration. A midwater joint 55 is provided between the upper and lower parts and includes at least three shear plates 58 disposed in vertical planes between the peripheral vertical surfaces 50a of the vertical leg or legs of the upper part and the peripheral surfaces 51a of the discrete legs of the lower part. The leg or legs of the upper part may extend down from the midwater joint to a position between the midwater joint and the seabed.