This paper examines techniques that have been used to estimate potential output and finds them wanting. We suggest a simple multivariate-filtering technique that is a generalization of the Hodrick-Prescott univariate filter. In univariate filters, only information about a variable itself is used in eliminating noise in order to obtain an estimate of the underlying trend. We suggest a generalization, wherein other information is used to sharpen the identification of potential output. For example, we note that, if movements in potential output have a different effect on inflation than do cyclical movements in output, then information on inflation may be useful in identifying potential output. The prospects for improving measures of potential output by using this and other information in the multivariate filter are demonstrated through Monte Carlo experiments. Evidence is also presented contrasting the results of using the multivariate filter on the historical Canadian data with the results from the Hodrick-Prescott filter and other, more traditional methods of estimating potential output. We argue that the multivariate filter has advantages over quasi-structural models of potential output because it can exploit general information from economic theory about what information might be useful, without imposing restrictions from imperfect representations of the true structure.