We study minimaxity of shrinkage estimators of location vectors under a wide class of concave loss functions. In particular, we show that many estimators of the James-Stein or Baranchik-type form, which dominate the “usual” estimator under the usual quadratic loss, also dominate under these concave losses. The distributions studied are multivariate normal with covariance equal to a known multiple of the identity, normal distributions with covariance equal to an unknown scale times the identity, and general scale mixtures of normal distributions with an unknown scale.