Methods and apparatus for spectrum-based endpointing. An endpointing method includes selecting two or more reference spectra. Each reference spectrum is a spectrum of white light reflected from a film of interest on a first substrate and has a thickness greater than a target thickness. The reference spectra is selected for particular spectra-based endpoint determination logic so that the target thickness is achieved when endpoint is called by applying the particular spectra-based endpoint logic. The method includes obtaining two or more current spectra. Each current spectrum is a spectrum of white light reflected from a film of interest on a second substrate when the film of interest is being subjected to a polishing step and has a current thickness that is greater than the target thickness. The method includes determining, for the second substrate, when an endpoint of the polishing step has been achieved.