In this article we propose a simple and efficient method of estimating welfare measures in an n-equation system. We also estimate the variance of these measures. The accuracy and convergence properties of our approach are studied: the algorithm converges quadratically. This is a distinct improvement over the Vartia algorithm which converges linearly. We demonstrate the method by evaluating the welfare consequences of price changes in the provision of health care. The GAUSS code, which is very short, is included.