Two examples where the fit to a periodogram fails (left panels) and the corresponding denoised multitaper spectrum leads to a good fit (right panels). The thick solid lines indicate the fits of the multitaper spectra, and the dotted lines indicate the central frequency of the fitted mode. Top row: Failure to converge (numerical flag), ﹩\ell =65﹩, ﹩m=-64﹩, ﹩n=9﹩. Bottom row: Fitted frequency error is larger than half the first guess width (heuristic flag), ﹩\ell =65﹩, ﹩m=-61﹩, ﹩n=4﹩.