In the talk we will discuss how imposing SO(10)-inspired conditions on the Dirac neutrino mass matrix and an explanation of the matter-antimatter asymmetry of the Universe with the minimal scenario of leptogenesis, there exists a class of solutions that imply interesting constraints on the low energy neutrino parameters. If one further imposes a condition of independence of the final asymmetry of the initial conditions (strong thermal leptogenesis), this is satisfied only by a restricted subset resulting into quite sharp predictions on the neutrino masses and mixing parameters. These predictions will be tested during next years by (currently or close future) data taking experiments.