This paper studies decision theoretic properties of benchmarked estimators which are of some importance in small area estimation problems. Benchmarking is intended to improve certain aggregate properties (such as study-wide averages) when model based estimates have been applied to individual small areas. We study admissibility and minimaxity properties of such estimators by reducing the problem to one of studying these problems in a related derived problem. For certain such problems we show that unconstrained solutions in the original (unbenchmarked) problem give unconstrained Bayes, minimax or admissible estimators which automatically satisfy the benchmark constraint. We illustrate the results with several examples. Also, minimaxity of a benchmarked empirical Bayes estimator is shown in the Fay-Herriot model, a frequently used model in small area estimation.