Since the introduction of simultaneously calibrated radial velocity (RV) spectrographs, the practice of using standard RV stars to correct for systematic zero-point variations was largely abandoned. However, in two recent works we show that the RV precision of even state-of-the-art instruments, such as HARPS/ESO and HIRES/Keck, can be further improved by using this technique. By averaging the RVs of different quiet stars that were observed each night, we calculate instrumental nightly zero-point RVs, and find small (~1 m/s) but significant variations, as well as small average intra-night drifts, in both HARPS and HIRES. Correcting HARPS’ RVs for these small systematic effects is found to improve its overall precision by few percent, in particular for data taken after the 2015 intervention. For HIRES, the main zero-point offset is found to be caused by the 2004 intervention (~1.5 m/s). Correcting HIRES’ RVs for this, and the other systematic effects we find, suppresses some spurious signals in stellar RV periodograms, mainly at low frequencies. Most importantly, the correction makes both data sets more consistent over timescales of years, which can facilitate the search for low-amplitude long-period orbital signatures of low-mass temperate planets.