If the only contribution to neutrinoless double beta decay (0νβ β) are neutrino masses its discovery may be very difficult, especially if neutrinos present a normal hierarchy spectrum. However, this is not the only possibility; 0νβ β can in general produce electrons of either chirality, in contrast with the neutrino induced 0νβ β which predicts two left-handed electrons. Using an effective Lagrangian approach we classify the lepton number violating (LNV) effective operators with two leptons of either chirality but no quarks, ordered according to the magnitude of their contribution to 0νβ β. We point out that, for each of the three chirality assignments, eLeL, eLeR and eReR , there is only one LNV operator of the corresponding type to lowest order, and these have dimensions 5, 7 and 9, respectively. Neutrino masses are always induced by these extra operators but can be delayed to one (dimension 7) or two loops (dimension 9). Under the assumption that 0νβ β is dominated by the operators of dimension 7 or 9 we find that the scale of new physics should be relatively low (. 30 TeV). We also list the SM additions generating these operators upon integration of the heavy modes, and discuss simple realistic examples of renormalizable theories for each case. The phenomenology of a model giving rise to the dimension 9 operator has been analyzed with some detail: if 0νβ β is going to be seen in the next round of experiments, the doubly charged scalars of the model could be seen at the LHC and lepton flavour violating (LFV) rates could be at the reach of foreseen experiments. Moreover neutrino masses, which arise at two loops, display a very particular structure and are strongly constrained, in fact, sin2 θ13 & 0.008, when µ → eee is required to lie below its present experimental limit.