Most descriptions of the color-rendering properties of light sources are based on the calculation of color differences for a number of test colors between the light source and a reference source. The CIE color-rendering index (CRI) is a single number based on the average color difference for eighht test colors. Ever since its introduction the CRI has been discussed and several suggestions have been made to improve the description of the CRI such as color preference index. color appearance data and color discrimination index. New lighting technologies such as LEDs can have spectral power distributions consisting of narrow spectral bands in the red, green and blue region of the spectrum. There are indications that the CRI does not always provide a reliable description of the color-rendering properties of these LED based light sources. In this article the principal elements of the CRI calculation are analyzed and their influence on the color-rendering description will be discussed. The focus of the analysis has been on the selection of object colors. Principally the color-rendering description of a light source should not depend on the set of colors chosen for the calculation. From our analysis requirements for such color sets are given. (C) 2010 Wiley Periodicals, Inc. col Res Appl, 35, 85-93, 2010: Published online 7 January 2010 in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.20546