A database of 140 diesel fuels having cetane numbers in the range of 10-70 points; densities at 15 degrees C; and distillation characteristics according to ASTM D-86 T-10%, T-50%, and T-90% was used to develop new procedures for predicting diesel cetane numbers by application of the least-squares method (LSM) using MAPLE software and an artificial neural network (ANN) using MATLAB. The existing standard methods of determining cetane-index values, ASTM D-976 and ASTM D-4737, which are correlations of the cetane number, confirmed the earlier conclusions that these methods predict the cetane number with a large variation. The four-variable ASTM D-4737 method was found to better approximate the diesel cetane number than the two-variable ASTM D-976 method. The developed four cetane-index models (one LSM and three ANN models) were found to better approximate the middle-distillate cetane numbers. Between 4% and 5% of the selected database of 140 middle distillates were samples with differences between their measured cetane numbers and the cetane-index values predicted by the four new procedures was higher than the specified reproducibility limit in the standard for measuring cetane number, ASTM D-613. In contrast, the cetane-index values calculated in accordance with standards ASTM D-976 and ASTM D-4737 demonstrated that 18% and 16% of the selected database of 140 middle distillates, respectively, were samples with differences between their measured cetane numbers and predicted cetane-index values higher than the specified reproducibility limit in standard ASTM D-613. The ASTM D-4737 method, LSM, and three ANN models were tested against 22 middle distillates not included in the database of 140 diesel fuels. The LSM cetane index showed the best cetane-number prediction capability among all of the models tested.