Recently-proposed modifications to the CIECAM16 color appearance model require an update to its corresponding uniform color space, CAM16-UCS, in order to ensure that the formulas continue to predict the available color difference data. Theoretical and statistical inconsistencies in the current CAM16-UCS formulas are also discussed and addressed by the proposed revisions. The STRESS metric is used to derive new formulas for CAM16-UCS and to evaluate the performance of these formulas in comparison to existing uniform color spaces or color difference formulas on a common color difference dataset.