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We investigated the stellar population properties of a sample of 1858 massive compact galaxies (MCGs) extracted from the Sloan Digital Sky Survey (SDSS). Motivated by previous results showing that older compact galaxies tend to have larger velocity dispersion at fixed stellar mass, we used the distance to the σe versus R e and M ⋆ versus σe relations as selection criteria. We found that MCGs are old (≳10 Gyr), α-enhanced ([α/Fe] ∼ 0.2), and have solar to supersolar stellar metallicities. Metallicity increases with σe, while age and [α/Fe] do not vary significantly. Moreover, at fixed σe, metallicity and stellar mass are correlated. Compared with a control sample of typical quiescent galaxies, MCGs have, on average, lower metallicities than control sample galaxies (CSGs) of similar σe. For σe ≲ 225 km s−1, MCGs are older and more α-enhanced than CSGs, while for higher σe ages and α-enhancement are similar. The differences in age and α-enhancement can be explained by lower σe CSGs being an amalgam of quiescent galaxies with a variety of ages. The origin of the differences in metallicity, however, is not clear. Lastly, we compared the stellar mass within the region probed by the SDSS fibre finding that, at fixed fibre velocity dispersion, MCGs have lower stellar masses on average. Since the velocity dispersion is a tracer of the dynamical mass, this raises the possibility that MCGs have, on average, a bottom-heavier initial mass function or a larger dark matter fraction within the inner ∼1−2 kpc. [ABSTRACT FROM AUTHOR]