We compare two approaches for estimating state-level public opinion: disaggregation by state of national surveys and a simulation approach using multilevel modeling of individual opinion and poststratification by population share. We present the first systematic assessment of the predictive accuracy of each and give practical advice about when and how each method should be used. To do so, we use an original data set of over 100 surveys on gay rights issues as well as 1988 presidential election data. Under optimal conditions, both methods work well, but multilevel modeling performs better generally. Compared to baseline opinion measures, it yields smaller errors, higher correlations, and more reliable estimates. Multilevel modeling is clearly superior when samples are smaller-indeed, one can accurately estimate state opinion using only a single large national survey. This greatly expands the scope of issues for which researchers can study subnational opinion directly or as an influence on policymaking.