ABSTRACT The accretion of planetary debris into the atmospheres of white dwarfs leads to the presence of metal lines in their spectra. Cool metal-rich white dwarfs, which left the main sequence many Gyr ago, allow the study of the remnants of the oldest planetary systems. Despite their low effective temperatures (Teff), a non-negligible amount of their flux is emitted in the near-ultraviolet (NUV), where many overlapping metal lines can potentially be detected. We have observed three metal-rich cool white dwarfs with the Space Telescope Imaging Spectrograph (STIS) onboard the Hubble Space Telescope, and compare the results determined from the NUV data with those previously derived from the analysis of optical spectroscopy. For two of the white dwarfs, SDSS J1038−0036 and SDSS J1535+1247, we find reasonable agreement with our previous analysis and the new combined fit of optical and NUV data. For the third object, SDSS J0956+5912, including the STIS data leads to a 10 per cent lower Teff, though we do not identify a convincing explanation for this discrepancy. The unusual abundances found for SDSS J0956+5912 suggest that the accreted parent body was composed largely of water ice and magnesium silicates, and with a mass of up to ≃ 2 × 1025 g. Furthermore, SDSS J0956+5912 shows likely traces of atomic carbon in the NUV. While molecular carbon is not observed in the optical, we demonstrate that the large quantity of metals accreted by SDSS J0956+5912 can suppress the C2 molecular bands, indicating that planetary accretion can convert DQ stars into DZs (and not DQZs/DZQs).