An alternative algorithm for solving random regression test-day models was developed to allow use of those models for extremely large data sets such as the US database for dairy records. The algorithm also facilitates integration of data from 305-day records when no test-day records are available and simplifies development of an index for lactation performance that includes genetic differences in lactation curve (persistency) and genetic effects of parity (maturity rate). Equations are solved in two iterative steps: 1) estimation or update of regression coefficients based on test-day yields for a given lactation and 2) estimation of fixed and randon effects on those coefficients. (...)