  We calculate the baryon asymmetry of the Universe in thermal leptogenesis
beyond the usual lightest right-handed (RH) neutrino dominated scenario (N_1DS)
and in particular beyond the hierarchical limit (HL), M_1 << M_2 << M_3, for
the RH neutrino mass spectrum. After providing some orientation among the large
variety of models, we first revisit the central role of the N_1DS, with new
insights on the dynamics of the asymmetry generation and then discuss the main
routes departing from it, focusing on models beyond the HL. We study in detail
two examples of `strong-strong' wash-out scenarios: one with `maximal phase'
and the limit of very large M_3, studying the effects arising when
delta_2=(M_2-M_1)/M_1 is small. We extend analytical methods already applied to
the N_1DS showing, for example, that, in the degenerate limit (DL), the
efficiency factors of the RH neutrinos become equal with the single decay
parameter replaced by the sum. Both cases disprove the misconception that close
RH neutrino masses necessarily lead to a final asymmetry enhancement and to a
relaxation of the lower bounds on M_1 and on the initial temperature of the
radiation-dominated expansion. We also explain why leptogenesis tends to favor
normal hierarchy compared to inverted hierarchy for the left-handed neutrino
masses.
