The intrinsic spectrally resolved sensitivity (ISRS) of color rendering indices (CRIs) is investigated by using spectral loss simulations. It is demonstrated that R(a) exhibits large sensitivities around 444, 480, 564, and 622 nm, while for R(9) the sensitivity peaks are around 461, 581 and 630 nm, which all shift slightly with the correlated color temperature. If considering the ISRS as a bridge between the spectral power distribution of LED and its CRI, one could obtain a high CRI by minimizing the deviation between the shapes of the illuminant spectrum and the reference spectrum, both after modulations by the ISRS as a weighting function. This approach, recommended as a guideline for the spectra design aiming at a high CRI, is described and justified in depth via a mathematical model. This method is spectra-oriented and could largely facilitate the spectra design.