ABSTRACT We present a new set of surface brightness fluctuation (SBF) spectra computed with the E-MILES stellar population synthesis models. The model SBF spectra cover the range λλ1680–50 000 at moderately high resolution, all based on extensive empirical stellar libraries. The models span the metallicity range $-2.3\le \mbox{$\mbox{[M/H]}$}\le +0.26$ for a suite of intial mass function types with varying slopes. These predictions can complement and aid fluctuation magnitude studies, permitting a first-order approximation by applying filter responses to the SBF spectra to obtain spectroscopic SBF magnitudes. We provide a recipe for obtaining the latter and discuss their uncertainties and limitations. We compare our spectroscopic SBF magnitudes to photometric data of a sample of early-type galaxies. We also show that the SBF spectra can be very useful for constraining relevant stellar population parameters. We find small (<5 per cent) mass fractions of extremely metal-poor components ($\mbox{$\mbox{[M/H]}$}\lt -1$) on the top of the dominant, old, and metal-rich stellar population. These results put stringent constraints on the early stages of galaxy formation in massive elliptical galaxies. This is remarkable given the high degree of degeneracy of the standard spectral analysis to such metal-poor stellar populations in the visible and in the near-infrared. The new SBF models show great potential for exploiting ongoing surveys, particularly those based on narrow-band filters.