We calculate the baryon asymmetry of the Universe in thermal leptogenesisbeyond the usual lightest right-handed (RH) neutrino dominated scenario(N1DS) and in particular beyond the hierarchical limit (HL), , for the RH neutrino mass spectrum. After providing some orientationamong the large variety of models, we first revisit the central role of theN1DS, with new insights on the dynamics of the asymmetry generation, and then discuss the mainroutes departing from it, focusing on models beyond the HL. We study in detail two examplesof ‘strong–strong’ wash-out scenarios: one with ‘maximal phase’ and the limit of very largeM3, studying the effects arising when is small. We extend analytical methods already applied to theN1DS showing, for example, that, in the degenerate limit (DL), the efficiency factors of the RHneutrinos become equal, with the single decay parameter replaced by the sum. Bothcases disprove the misconception that close RH neutrino masses necessarily leadto a final asymmetry enhancement and to a relaxation of the lower bounds onM1 and on the initial temperature of the radiation-dominated expansion. We also explain whyleptogenesis tends to favour normal hierarchy compared to inverted hierarchy for theleft-handed neutrino masses.