In a cost-effectiveness analysis using clinical trial data, estimates of the between-treatment difference in mean cost and mean effectiveness are needed. Several methods for handling censored data have been suggested. One of them is inverse-probability weighting, and has the advantage that it can also be applied to estimate the parameters from a linear regression of the mean. Such regression models can potentially estimate the treatment contrast more precisely, since some of the residual variance can be explained by baseline covariates. The drawback, however, is that inverse-probability weighting may not be efficient. Using existing results on semi-parametric efficiency, this paper derives the semi-parametric efficient parameter estimates for regression of mean cost, mean quality-adjusted survival time and mean survival time. The performance of these estimates is evaluated through a simulation study. Applying both the new estimators and the inverse-probability weighted estimators to the results of the EVALUATE trial showed that the new estimators achieved a halving of the variance of the estimated treatment contrast for cost. Some practical suggestions for choosing an estimator are offered.