There is a trade-off between the signal level and bandwidth of the atomic lines in laser-induced breakdown spectroscopy (LIBS). The LIBS plasma plume is a dense plasma, with linewidths of spectral features enlarged by Stark broadening. Narrow linewidths can be detected at delays of some μs with respect to the laser pulse, but this comes at the cost of low signal intensity. This demand becomes urgent when spectral separation is necessary, as in the application of LIBS for in situ detection of atomic deuterium (D) and atomic tritium (T) in walls exposed to the plasma of a Tokamak. The D and T Balmer lines need to be well separated from the atomic hydrogen (H) lines that are present as contaminants in the LIBS spectra. Clearly, solving for the signal-bandwidth tradeoff can be of more general interest than the Balmer lines issue only. In this work, we report an investigation of LIBS signal enhancement with a low-pressure (some Torr), pulsed glow-discharge. The discharge produces a low-density plasma that has a negligible effect on the linewidth. The possibility of signal enhancement instead relies on the long duration of the discharge compared with that of the plume, allowing for long time-integration of the atomic emissions. The concept can be stressed to the limit in which the laser shot just ablates the material, whereas the electronic excitation of the material is obtained by the non-equilibrium gas discharge ignited in a background gas in the region where the laser-induced plasma plume expands.