Lactation records of cows born since 1964 were used to compute Cow Indexes (CI) for 581,519 Holsteins and 352,758 Jerseys. CI were used to predict Modified Contemporary Deviations (MCD) of daughters at three levels each of herd mean (µ) and standard deviation (σ), and regressions were compared to expected values. For Holsteins, regressions were greater than expected in herds with average µ or high σ, suggesting that heritability (h²) should be higher for cows in those herds. Heritability estimates agreed with observed regressions for herd σ (h2 of .178, .193, and . 206 as herd σ increased) but not for herd µ (h² of . 222, .163, and .206). For Jerseys, regression results indicated that h² should increase with herd µ, but there was no trend for herd σ. Heritability estimates agreed with the observed regressions for µ (h² of .246, .291, and .331) but not for σ, as h² increased substantially ( .254, .293, and .371) as herd σ increased. Eight adjustments were made for CI: two varied h² to adjust for genetic effects, two adjusted MCD for environmental effects, and four were combinations of these. For Holsteins, regressions of daughter MCD on darn CI were greater than expected for all CI, but regressions of son MCD on darn CI were less than expected. Rankings of CI, based on R² , differed considerably for the three groups examined (all daughters, daughters of elite cows, and sons). For Jerseys, CI of elite darns predicted offspring MCD as expected, but for several CI, regressions for all daughters were less than expected. There were smaller differences in rankings of CI than for Holsteins. Under the assumption that large true breed differences are unlikely, the best CI for both breeds had MCD standardized to a common variance, with h² of .20. This was nearly optimal for Jersey groups, although less than optimal for Holsteins. This CI adjusted for environmental effects of herd a, ignoring differences in genetic variation. It decreased differences among CI for cows in high variance herds, and increased differences in low variance herds. / Ph. D.