The estimation of a multivariate mean is considered under natural modifications of balanced loss functions of the form: (i) , and (ii) , where is a target estimator of . After briefly reviewing known results for original balanced loss with identity or , we provide, for increasing and concave and which also satisfy a completely monotone property, Baranchik-type estimators of which dominate the benchmark for either distributed as multivariate normal or as a scale mixture of normals. Implications are given with respect to model robustness and simultaneous dominance with respect to either or .