An offshore multiple tendon compliant buoyant tower construction for well operations in which a plurality of tendons are arranged in parallel, vertical, closely spaced assembled relation and have top and bottom ends, the bottom ends being connected to a base module at the sea floor, the top ends being connected to a buoyant structure which includes conductor tubes therein for each of said tendons and which serves to restrict bending of the top portion of said tendons to provide a relatively stiff, unbending, noncompliant tendon top portion which extends below the sea surface, the portion of the assembled tendons below the stiff to portion being relatively compliant; the buoyant structure imparting tension to said plurality of assembled tendons at the top ends thereof whereby the tensioned tendons provide lowering of the effective center of gravity of the tower construction below the center of buoyancy and whereby cyclic stresses in the assembled tendons resulting from roll or bending of the tower construction is reduced.