There is compelling, largely agreed-upon evidence that the CIE Color Rendering Index (CRI) is not a sufficiently accurate measure of the average color rendering difference between two different spectral irradiance distributions. This has become particularly evident with the consideration of white light sources employing several narrow band light emitters. In this presentation an approach is suggested for reducing the error, based on consideration of certain meta-standards for evaluation of proposed CRI calculation methods. Here we focus mainly on one such meta-standard-the idea that the spectral sensitivity of the CRI should be reasonably uniform and largely independent of the details of the selected sample set. A key problem with the current CRI calculation method, and some suggested improvements, has been their lack of this important characteristic. By employing this guiding principle, we have devised an improved sample set that substantially eliminates the problem of non-uniform spectral sensitivity.