We present the detection of nuclear stellar discs in the low-luminosity elliptical galaxies, NGC 4458 and 4478, which are known to host a kinematically decoupled core. Using archival Hubble Space Telescope imaging, and available absorption line-strength index data based on ground-based spectroscopy, we investigate the photometric parameters and the properties of the stellar populations of these central structures. Their scalelength, h, and face-on central surface brightness, μc0, fit on the μc0–h relation for galaxy discs. For NGC 4458, these parameters are typical for nuclear discs, while the same quantities for NGC 4478 lie between those of nuclear discs and the discs of discy ellipticals. We present Lick/Image Dissector Scanner (IDS) absorption line-strength measurements of Hβ, Mgb and 〈Fe〉 along the major and minor axes of the galaxies. We model these data with simple stellar populations that account for the α/Fe overabundance. The counter-rotating central disc of NGC 4458 is found to have similar properties to the decoupled cores of bright ellipticals. This galaxy has been found to be uniformly old despite being counter-rotating. In contrast, the cold central disc of NGC 4478 is younger, richer in metals and less overabundant than the main body of the galaxy. This points to a prolonged star formation history, typical of an undisturbed disc-like, gas-rich (possibly pre-enriched) structure.