During the early 1970s the offshore market in the North Sea was growing rapidly. Due to discoveries of natural reserves and development of the oil price, the oil and gas industry developed and deployed many bottom founded offshore structures in the North Sea. Apart from steel jacket structures, many concrete gravity based structures (CGBSs) were constructed. In the coming decades many of the fields with these CGBSs approach the end of their lifetime and must be decommissioned. However, currently no solid solution for the removal of these concrete substructures is available. The introduction of Allseas’ Pioneering Spirit and her capabilities could provide new possibilities for the decommissioning of CGBSs. The Pioneering Spirit is designed for the decommissioning of platforms and its substructure using a unique “single lift” technique. A complete removal of the concrete substructure using this single lift technique is, due to its constructive condition, a perilous operation. However, the decommissioning regulations allow a partial removal of the concrete legs above a water depth of 55 meters. At this water depth a cut is made in the legs and after cutting the Pioneering Spirit can perform a lift of the leg using the Jacket Lift System (JLS). During this removal operation various problems may arise. In this study the main technical difficulties of the partial removal operation are identified. A focus is laid on the difficulties during the lifting phase. The hoisting speed of the JLS is relatively slow compared to the ship motions. This can result in a rebound of the leg during the initial lifting phase. Damage to the leg and a probable damage to the part of the GBS where the oil storage was located may then occur. The objective in this study is to design a solution for the initial lifting phase and analyze the feasibility of this concept. An adequate fast lifting solution after cut-off could overcome the problems associated with the rebound of the concrete legs. The designed solution for fast lifting is based on the concept of a passive heave compensator (PHC). To gain insight into the feasibility of this concept a model has been made in MATLAB/Simulink. Input data for the simulation model are mechanical dimension parameters and physical pressure parameters. By altering the parameters an estimation of the motions of the leg and hence the feasibility of the concept is determined.