these cases, in order to fit the narrow [H$\beta$]{}component, we retain the flux and centroid limits described above but relax the line width constraint, and instead impose an (rather arbitrary) upper limit of $\sigma \leq 550$ [km s$^{-1}$]{}.

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Errors and Uncertainties
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In objects with minimal galaxy contamination, the uncertainty in the flux of the optical continuum is dominated by the proper removal of  emission and errors in the continuum slope. We use the measured  flux at 5100 Å to estimate the uncertainty contributed by our decomposition. To estimate errors resulting from the power-law fit, we average the fluxes obtained when the slope of the power law is allowed to increase or decrease by one standard deviation, as obtained from the fit. The final adopted error is the quadrature sum of the  and slope errors, although the latter usually dominates. Typical errors are $\sim 0.04$ dex. The largest source of uncertainty in measurements of line flux comes from the placement of the continuum level. We estimate our uncertainty by adjusting the continuum level by one standard deviation above and below the nominal best-fit level of the continuum, and then recalculating the line flux. Typical errors in the 