A set of invertible non-linear transforms was derived that adjusts Wpt (Waypoint) coordinates (based on Wpt normalization) to and from a perceptually more uniform coordinate system (WLab or Waypoint-Lab) than that provided by Wpt that allows for the advantageous features of Wpt to be directly applied to situations where other standard color spaces are typically used. The proposed transformations were found by optimizing for perceptual uniformity over both large and small color difference scales. The Munsell color order system was used as a representation for optimizing large-scale perceptual uniformity. Correlations with Munsell value, chroma and hue along with comparisons with CIELAB and CAM02-UCS were used to correct and assess overall large-scale uniformity. The E*(94) color difference formula was used for optimization purposes for small-scale uniformity. A STRESS analysis was applied to compare color differences based on Euclidean WLab distances with color differences based upon E*(ab), E*(94), E-00, DIN99o, CIECAM02, and CAM02-UCS. It was found that WLab is a reasonably uniform material color equivalency space with small Euclidean WLab distances not being statistically different from E*(94), E-00, and Euclidean distances of DIN99o and CAM02-UCS under reference observing conditions. (c) 2014 Wiley Periodicals, Inc. Col Res Appl, 40, 550-563, 2015