In a typical comparative clinical trial, the longitudinal (baseline and post-baseline) data, possibly incomplete due to dropouts, are commonly analyzed using likelihood-based methods (e.g., REML) that assume multivariate normality of the response vector, conditional on potential covariates. If the normality assumption is untenable, semi-parametric methods like generalized estimating equations (GEE) or weighted GEE (WGEE) are sometimes used. With a goal of retaining good performance under normality, but significantly increasing efficiency under non-normality, we present alternate approaches that involve multiple imputation of missing values followed by an outlier-resistant parametric analysis, all easily implemented using existing SAS procedures. The efficiency gains using the new methods versus REML, GEE and WGEE are quantified using simulations, and illustrated using a real example.