Flavor effects in leptogenesis reduce the region of the see-saw parameter space where the final predictions do not depend on the initial conditions, the strong wash-out regime. In this case we show that the lowest bounds holding on the lightest right-handed (RH) neutrino mass and on the reheating temperature for hierarchical heavy neutrinos, do not get relaxed compared to the usual ones in the one-flavor approximation, M_1 (T_reh) \gtrsim 3 (1.5) x 10^9 GeV. Flavor effects can however relax down to these minimal values the lower bounds holding for fixed large values of the decay parameter K_1. We discuss a relevant definite example showing that, when the known information on the neutrino mixing matrix is employed, the lower bounds for K_1 \gg 10, are relaxed by a factor 2-3 for light hierarchical neutrinos, without any dependence on \theta_13 and on possible phases. On the other hand, going beyond the limit of light hierarchical neutrinos and taking into account Majorana phases, the lower bounds can be relaxed by one order of magnitude. Therefore, Majorana phases can play an important role in leptogenesis when flavor effects are included.