A system for offloading LNG (liquified natural gas) from a tanker (26) in shallow waters, for regasing, or heating the offloaded LNG to produce gaseous hydrocarbons, or gas, for pressurizing the gas, and for flowing the gas to an onshore station (56), includes a structure that is fixed to the sea floor and projects above the sea surface and aids in mooring the tanker. In one system, the structure that is fixed to the sea floor is a largely cylindrical tower (12) with a mooring yoke (20) rotatably mounted on its upper end. A floating structure (14) such as a barge that weathervanes, has a bow end pivotally connected to a distal end of the yoke, so the barge is held close to the tower but can drift around the tower with changing winds, waves and currents. The tanker is moored to the barge so the barge and tanker form a combination that weathervanes as a combination. Regas and pressurizing equipment (32, 34) for heating and pressuring the LNG, and any crew quarters (36), are all located on the barge, so a low cost tower can be used. In another system, the structure is a breakwater (180).