ABSTRACT The proper quantitative NMR (qNMR) setup requires efficient relaxation of all active nuclei between scans. To achieve this, the spectroscopist has to know the longitudinal relaxation constant ( ) for each nucleus involved in the experiment and set the interscan delay to at least five times the longest . The is most commonly measured using the inversion–recovery method, which is essentially the acquisition of a series of spectra with increasing delay between 180° and 90° pulses. Unfortunately, the inversion–recovery experiment can last hours if a long is expected. In this paper, we show how to perform it faster by employing sweeping apparatus for polarisation enhancement (SWAPE)—an apparatus that can shift the sample vertically synchronously to the pulse sequence. In brief, the inversion recovery occurs in the sample parts that are shifted away from the RF coil, while other spins in an active volume are excited and measured. This way, the long, passive delays are avoided, and the experiment is shortened several times. We demonstrate its potential on the formic acid sample, a commonly used qNMR reference standard. The resulting s is in good agreement with the one measured using the conventional approach, s, requiring approximately 5.8 times less acquisition time.