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The electrostatics of fully depleted MOS devices such as double- and triple-gate MOSFETs are highly dependent on the thickness of the silicon-on-insulator film in the channel. Scaling these devices to their ultimate limits makes it necessary to scale the channel thickness into a regime where quantum confinement effects negatively impact the electrical transport properties of the film. We use the application of uniaxial mechanical strain to investigate electron mobility in films where mobility has been degraded by quantum size effects. We find that these films exhibit more mobility enhancement from strain than do thick films, indicating that the strain increases mobility conventionally and mitigates the mechanism that causes mobility degradation in thin films.