Two methods developed to improve regression estimation in double sampling under the superpopulation model approach are examined. One method proposes the use of an alternative double sample regression estimator. The other method recommends the use of nonrandom, purposive subsampling plans. Both methods aim to reduce the mean squared errors of regression estimators in double sampling. A major criticism against the superpopulation model approach is its strong dependence on the correctness of the assumed model. Thus, two purposive subsampling plans were considered. The first plan designed subsamples based on the assumption that the superpopulation model was a first order linear model. The second plan selected subsamples that guarded against the occurrence of a second order model. As expected, the designed subsamples without protection can be very sensitive to the presence of a second order linear model. On the other hand, the designed subsamples with protection rendered the double sample regression estimators robust not only to a second order superpopulation model but also fairly robust to other slight model deviations such as variance misspecification. Therefore the use of designed subsamples with protection against a second order model is suggested whenever a first order superpopulation model is uncertain. Under designed subsamples with or without protection, the alternative double sample regression estimator is not found to be more efficient than the usual double sample regression estimator found in most sampling textbooks . However, the alternative double sample regression estimator has shown itself to be more efficient under simple random subsampling when the correlation between variables is weak and subsamples are small. / Ph. D.