Finding optimal compression levels for diagnostic imaging is not an easy task. Significant compressibility variations exist between modalities, but little is known about compressibility variations within modalities. Moreover, compressibility is affected by acquisition parameters. In this study, we evaluate the compressibility of thousands of computed tomography (CT) slices acquired with different slice thicknesses, exposures, reconstruction filters, slice collimations, and pitches. We demonstrate that exposure, slice thickness, and reconstruction filters have a significant impact on image compressibility due to an increased high frequency content and a lower acquisition signal-to-noise ratio. We also show that compression ratio is not a good fidelity measure. Therefore, guidelines based on compression ratio should ideally be replaced with other compression measures better correlated with image fidelity. Value-of-interest (VOI) transformations also affect the perception of quality. We have studied the effect of value-of-interest transformation and found significant masking of artifacts when window is widened.