Aims. We show that the line broadening in quiescent solar prominences is mainly due to non-thermal velocities. Methods. We have simultaneously observed a wide range of optically thin lines in quiescent prominences, selected for bright and narrow Mg b emission without line satellites from macro-shifts. Results. We find a ratio of reduced widths, Δλ D /λ 0 , of Hγ and Hδ of 1.05 ± 0.03, which can hardly be attributed to saturation, since both are optically thin for the prominences observed: τ γ ≤ 0.3, τ δ ≤ 0.15. We confirm the ratio of reduced widths of He 4772 (triplet) and He 5015 (singlet) of 1.1 ± 0.05 at higher significance and detect a width ratio of Mg b 2 and Mg 4571 (both from the triplet system) of 1.3 ± 0.1. Conclusions. The discrepant widths of lines from different atoms, and even from the same atom, cannot be represented by a unique pair [T kin ; V nth ]. Values of T kin deduced from observed line radiances using models indicate low temperatures down to T kin ≈ 5000 K. Non-thermal velocities, related to different physical states of the respective emitting prominence region, seem to be the most important line broadening mechanism.