Context. The secondary-to-primary B/C ratio is widely used for studying Galactic cosmic-ray propagation processes. The H-2/He-4 and He-3/He-4 ratios probe a different Z/A regime, which provides a test for the universality of propagation. Aims. We revisit the constraints on diffusion-model parameters set by the quartet (H-1, H-2, He-3, He-4), using the most recent data as well as updated formulae for the inelastic and production cross-sections. Methods. Our analysis relies on the USINE propagation package and a Markov Chain Monte Carlo technique to estimate the probability density functions of the parameters. Simulated data were also used to validate analysis strategies. Results. The fragmentation of CNO cosmic rays (resp. NeMgSiFe) on the interstellar medium during their propagation contributes to 20% (resp. 20%) of the H-2 and 15% (resp. 10%) of the He-3 flux at high energy. The C to Fe elements are also responsible for up to 10% of the He-4 flux measured at 1 GeV/n. The analysis of He-3/He-4 (and to a lesser extent H-2/He-4) data shows that the transport parameters are consistent with those from the B/C analysis: the diffusion model with delta similar to 0.7 (diffusion slope), V-c similar to 20 km s(-1) (galactic wind), V-a similar to 40 km s(-1) (reacceleration) is favoured, but the combination delta similar to 0.2, V-c similar to 0, and V-a similar to 80 km s(-1) is a close second. The confidence intervals on the parameters show that the constraints set by the quartet data can compete with those derived from the B/C data. These constraints are tighter when adding the He-3 (or H-2) flux measurements, and the tightest when the He flux is added as well. For the latter, the analysis of simulated and real data shows an increased sensitivity to biases. Using the secondary-to-primary ratio along with a loose prior on the source parameters is recommended to obtain the most robust constraints on the transport parameters. Conclusions. Light nuclei should be systematically considered in the analysis of transport parameters. They provide independent constraints that can compete with those obtained from the B/C analysis.