We estimate the natural rate of interest for the US and the euro area in a semi-structural model comprising a Taylor rule. Our estimates feature key elements of Laubach and Williams (2003), but are more consistent with using conventional policy rules: we model inflation to be stationary, with the output gap pinning down deviations of inflation from its objective (rather than relative to a random walk). We relax some constraints on the correlation of latent factor shocks to make the original unobserved-components framework more amenable to structural interpretation and to reduce filtering uncertainty. We show that resulting natural rate metrics are more consistent with estimates from structural models.