In one aspect, a method of polishing includes polishing a substrate, and receiving an identification of a selected spectral feature and a characteristic of the selected spectral feature to monitor during polishing. The method includes measuring a sequence of spectra of light reflected from the substrate while the substrate is being polished, where at least some of the spectra of the sequence differ due to material being removed during the polishing. The method of polishing includes determining a value of a characteristic of the selected spectral feature for each of the spectra in the sequence of spectra to generate a sequence of values for the characteristic, fitting a function to the sequence of values, and determining either a polishing endpoint or an adjustment for a polishing rate based on the function.