Consider the independent Wishart matrices (S_{1} \sim W\left(\Sigma+\lambda \theta, q_{1}\right)) and (S_{2} \sim) (W\left(\Sigma, q_{2}\right)), where (\Sigma) is an unknown positive definite (p.d.) matrix, (\theta) is an unknown nonnegative definite (n.n.d.) matrix, and (\lambda) is a known positive scalar. For the estimation of (\theta), a class of estimators of the form (\hat{\theta}{\left(r{1}\right)}=(c / \lambda)\left{S_{1} / q_{1}-\varepsilon\left(S_{2} / q_{2}\right)\right}) ((c \geqslant 0, \varepsilon \leqslant 1)), uniformly better than the unbiased estimator (\hat{\theta}{U}=(1 / \lambda)\left{S{1} / q_{1}-\right.) (\left.S_{2} / q_{2}\right}), is derived (for the squared error loss function). Necessary and sufficient conditions are obtained for the existence of an n.n.d. estimator of the form (\hat{\theta}{(r, \varepsilon)}) uniformly better than (\hat{\theta}{U}). It turns out that such an n.n.d. estimator exists only under restrictive conditions. However, for a suitable choice of (c>0, \varepsilon>0), the estimator obtained by taking the positive part of (\hat{\theta}{(c, s)}) results in an n.n.d. estimator, say (\hat{\theta}{(c, f)+}), that is uniformly better than (\hat{\theta}{U}). Numerical results indicate that in terms of mean squared error, (\hat{\theta}{{c, c}}) performs much better than both (\hat{\theta}{v}) and the restricted maximum likelihood estimator (\hat{\theta}{\text {REML }}) of (\theta). Similar results are also obtained for the nonnegative estimation of (\operatorname{tr} \theta) and (\mathbf{a}^{\prime} \Theta \mathbf{a}), where (\mathbf{a}) is an arbitrary nonzero vector. For estimating (\Sigma), we have derived estimators that are claimed to be uniformly better than the unbiased estimator (\hat{E}{U}=S{2} / q_{2}) under the squared error loss function and the entropy loss function. We have been able to establish the claim only in the bivariate case. Numerical results are reported showing the risk improvement of our proposed estimators of (\Sigma). C 1994 Academic Press. Inc.