Genetic merits in first vs. later parity with correlations <1 were compared with official repeatability models using 88 million lactation records of 34 million cows for yield traits and fewer records for SCS and 2 cow fertility traits. Estimated genetic correlations of first with later parity ranged from 0.85 for SCS to 0.95 for fertility traits. These estimates were also applied to permanent environmental and herd-by-sire interaction effects that were constants within later parities and correlated with first-parity effects. Previous parity variance adjustments were removed. Computation took twice as many processors and required more iteration because of slightly slower convergence. All-parity merit combined first and later merit with weights of 0.33 and 0.67, respectively; genetic correlations of all-parity merit with either first or later merit ranged from 0.96 to 0.99. For all bulls progeny-tested since 1995, correlations with official evaluations were very high (0.999) for all traits. Correlations for the 2 most recent years of progeny-tested bulls were lower (0.991 for SCS to 0.997 for fat yield) because many of these bulls had only or mostly first-parity daughters. Computed reliabilities of these recent bulls averaged 3 percentage points less than official reliabilities. With the latest 5 yr of data removed, correlations of truncated and current evaluations were compared for the most recently proven US bulls. Correlations for SCS were higher for the new model than for the traditional model for Holsteins (0.875 vs. 0.867) and Brown Swiss (0.800 vs. 0.76) but not for Jerseys (0.822 vs. 0.826). Correlations for yield traits did not improve for any breed. In a separate test, modeling maturity effects using random regressions on parity gave predictions very similar to modeling first vs. later records. Modeling lactations as correlated traits can possibly reduce biases from early daughters and slightly improve stability for SCS when bulls transition from genomic predictions to observed daughter records, but did not improve correlations with future evaluations for other traits.