We present a general analysis that reveals new aspects of the leptogenesis bounds on neutrino masses and on the reheat temperature of the Universe. After revisiting a known effect coming from an unbounded term in the total CP asymmetry, we show that an unbounded term in the flavored CP asymmetries has a stronger impact. It relaxes the lower bound on the reheat temperature down to 10^8 GeV for (M_2-M_1)/M_1=O(1-100) and for a mild tuning of the parameters in the see-saw orthogonal matrix. We also consider the effect of the Higgs asymmetry, showing that it lowers the upper bound on the neutrino masses in the so-called fully flavored regime where classic Boltzmann equations can be used. Imposing independence of the initial conditions contributes to lower the upper bound on neutrino masses as well. We study the conditions for the validity of the usual N_1-dominated scenario and for the applicability of the lower bound on the lightest right-handed (RH) neutrino mass M_1. We find that except for the two effective RH neutrino scenario, recovered for M_3 >>10^14 GeV, and for values M_2 < O(10^11 GeV), the final asymmetry is more naturally dominated by the contribution from N_2-decays. Finally, we confirm in a general way that going beyond the hierarchical limit, the effect of washout addition makes the lower bound on M_1 more stringent for (M_2-M_1)/M_1=O(0.1).