The least squares method for computing colorimetric weighting tables is presented and its connection with the optimum weights method is investigated. Each requires solving three linear systems of equations with the same coefficient matrix but three different right hand side vectors. It is shown that the two methods have nearly the same performance when the wavelength interval of the data is large. The two methods however, will perform differently when is small. Comparisons are also made between the least squares method, the optimum weights method, the zero- and second-order weighting tables, and the ASTM weighting tables, both the original 1985 tables and the new 2013 Tables V and VI. The results show that the least squares method is the best for measurement intervals equal to or lower than 10 nm, and is competitive with the optimum weights method for 20 nm steps. The results presented in this article will contribute to the work of CIE Technical Committee TC1-71 Tristimulus Integration as it seeks to make recommendations for the calculation of tristimulus values. (c) 2015 Wiley Periodicals, Inc. Col Res Appl, 41, 125-142, 2016