In randomized experiments, analysis of covariance is used to increase precision of treatment comparisons. However, for factors that are observational (e.g., breed) or for covariates measured after treatments are applied, it may not be biologically meaningful to calculate treatment means adjusted to a common value of the covariate. For example, in beef cattle trials, it may not be meaningful to compare hot carcass weights of medium- and large-framed breeds adjusted to a common weaning weight because the breeds have naturally different mean weights at weaning. If done, this would typically result in an undesirable downward adjustment of mean carcass weight for the large-framed breed and upward adjustment of the mean carcass weight for the small-framed breed. However, it is desirable to evaluate the mean carcass weight for two diets, adjusted to a common weaning weight. Because of randomization, the expected weaning weights of animals on the two diets are equal and hence the only effect of covariance adjustment is to increase precision of the diet comparison. This paper presents the statistical methodology for estimating covariance adjusted means (termed partially adjusted means) when the levels of some of the factors are compared at a common value of the covariate but the levels of other factors are compared at differing values of the covariate. The methodology is extended to include several covariates, several factors, and arbitrary interactions among covariates, among factors, and between factors and covariates. These methods can be implemented using existing statistical software for linear models. Data are presented from an experiment in which hot carcass weight was recorded for beef cattle. Analyses of these data illustrate that adjusted means, partially adjusted means, and unadjusted means may differ substantially in magnitude, significance, and in the ranking of treatments.