Traditional techniques for balancing long, flexible, high-speed rotating shafts are inadequate over a full range of shaft speeds. This problem is compounded by limitations within the manufacturing process, which have resulted in increasing problems with lateral vibrations and hence increased the failure rates of bearings in practical applications. There is a need to develop a novel strategy for balancing these coupling shafts that is low cost, robust under typically long-term operating conditions and amenable to on-site remediation. This paper proposes a new method of balancing long, flexible couplings by means of a pair of balancing sleeve arms that are integrally attached to each end of the coupling shaft. Balance corrections are applied to the free ends of the arms in order to apply a corrective centrifugal force to the coupling shaft in order to limit shaft-end reaction forces and to impart a corrective bending moment to the drive shaft that limits shaft deflection. The aim of this paper is to demonstrate the potential of this method, via the mathematical analysis of a plain, simply supported tube with uniform eccentricity and to show that any drive shaft, even with irregular geometry and/or imbalance, can be converted to an equivalent encastre case. This allows for the theoretical possibility of eliminating the first simply supported critical speed, thereby reducing the need for very large lateral critical speed margins, as this requirement constrains design flexibility. Although the analysis is performed on a sub 15 MW gas turbine, it is anticipated that this mechanism would be beneficial on any shaft system with high-flexibility/shaft deflection.