The singlet states of nuclear spin-1/2 pairs often display extended lifetimes that can be an order of magnitude longer than conventional relaxation times. We show that, in favourable circumstances, acquisition of the NMR signal during an extended multiple spin-echo train, followed by suitable data processing, enhances the signal-to-noise ratio of singlet NMR by up to an order of magnitude. The achievable enhancement depends on the transverse relaxation time constant, the magnetic field inhomogeneity, and the acceptable degradation in digital spectral resolution. We use the combination of singlet NMR and multiple spin-echo data acquisition to study the low-field nuclear relaxation processes of (15)N-labelled nitrous oxide ((15)N(2)O) in solution. A general relaxation theory for coupled 2-spin-1/2 systems in low magnetic field is developed. Experimental trajectories of the nuclear spin observables are compared with theoretical expressions, including dipole-dipole and spin-rotation relaxation mechanisms. The estimated values of the spin-rotation tensors are compared with previous estimations from NMR and molecular beam electric resonance.