Abstract Covariate adjustment is often used in statistical analysis of randomized experiments to increase efficiency of estimators of treatment effects. In this paper, we study covariate adjustment based on the empirical and Euclidean likelihoods, and propose weighted versions that arise as natural alternatives. The weighted methods incorporate the auxiliary information that the covariates have equal means among the treatment groups due to randomization. We show that the empirical and the Euclidean likelihoods and their weighted versions are first order equivalent to Koch’s nonparametric covariance adjustment. Allowing the weights to be negative, the resulting pseudo Euclidean likelihood is equivalent to Koch’s method, and its weighted version can be viewed as a weighted version of Koch’s method. In a simulation study, we assess the finite sample properties of the proposed methods. The analysis of a clinical trial data set illustrates an application of these methods to a practical situation.