We explore possible correlations between light profile shapes, as parameterized by the Sérsic index n or the concentration index Cre(1/3), and relevant stellar population parameters in early-type galaxies. Mean luminosity-weighted ages, metallicities, and abundance ratios were obtained from spectra of very high signal-to-noise ratio and stellar population models that synthesize galaxy spectra at the resolution given by their velocity dispersions, σ, in combination with an age indicator (Hγσ) that is virtually free of the effects of metallicity. We do not find any significant correlation between n [or Cre(1/3)] and mean age or metallicity, but we do find a strong positive correlation of the shape parameters with Mg/Fe abundance ratio. This dependence is as strong as the Mg/Fe-σ and Cre(1/3)-σ relations. We speculate that early-type galaxies settle up their structure on timescales in agreement with those imposed by their Mg/Fe ratios. This suggests that the global structure of larger galaxies, with larger Mg/Fe ratios and shorter timescales, was already in place at high z, without experiencing a significant time evolution.