We suggest that the observed experimental data on relative double-strand break (dsb) yield as a function of radiation quality can act as valuable constraints in defining the type of energy deposition which causes this basic lesion in radiation biology. Both heavy-ion and alpha-particle data show sufficient trends for quantitative comparisons with calculation to be made. We use the technique of track-structure simulation and search for energy-deposition clusters (containing at least a given number of ionizations in a given diameter) whose relative frequencies (compared to sparsely ionizing radiation) correlate with the relative biological effects (RBEs) for dsb induction. We conclude that locally multiply damaged sites (LMDS) which cause dsb are probably energy depositions of at least two to five ionizations localized, respectively, in sites of diameters of 1-4 nm. Although our derived cluster sizes should be viewed in light of the quality of the experimental data and uncertainties in the computer simulations at the nanometre level, it is unlikely that these estimates of cluster sizes would change greatly.