An offshore drilling vessel includes a floating hull having a moonpool, a drilling tower positioned on the hull at or near the moonpool, a tubular string main hoisting device including a main hoisting winch and main cable connected to the main hoisting winch, a crown block mounted on the drilling tower, a travelling block suspended from the crown block in a multiple fall arrangement of the main cable, a mobile working deck and an integrated heave compensation system including a main cable heave compensation sheave in a path of the main cable between the main hoisting winch and the travelling block, a hydraulic sheave compensator connected to the main cable heave compensation sheave to provide a heave compensated motion of the travelling block, and a hydraulic deck compensator connected to the hull and to the mobile working deck to provide a heave compensated motion of the working deck relative to the hull within the heave compensation motion range.