Specialized statistical methods allow animal breeders to attain the greatest accuracy in the estimation of genetic merit of breeding animals from available data. Although the use of more data could provide even greater accuracy, data for all traits and from all places and all time may not be available in the same database. Statistical methods that work well with smaller data sets may not work at all with a large, combined data set. A selection index can provide an approximate method to combine information from separate sources. This approach would allow animal breeders to use better models and more data at the same time. Separate estimates of genetic merit can be combined through a selection index if a combined analysis of all data is not possible or efficient. Computation is fast but not exact if the reliabilities of the separate estimates are approximate, if the extent of overlap of the data sets is unknown, or if selection has occurred across the data sets. A selection index also can be used to combine single-trait evaluations into approximate multiple-trait evaluations or single-country rankings into multiple-country rankings for either males or females. Additional computer processing can be avoided by including parent evaluations as data and combining parent evaluations before evaluations of offspring. Exchange of sire and dam evaluations could provide a closer connection between national and international evaluations and may be more accurate than the current international model based on sire and maternal grandsire. Selection index methods may allow current international evaluations for bulls to be improved and to be extended to cows.