This article focuses on some very "fundamental threats" to future generations' leaving, and considers whether most essential interests of future persons not to be harmed can be construed as rights, and in particular as human rights, as much as present persons'. The framework refers essentially to a conceptual grammar of justice. Moreover, it is suggested to articulate rights through the lens of "disposability" and "non-disposability" principles. Finally, the article shows the reasons for separating what we owe to future persons under the challenge of those threats for humanity, i.e. a matter of justice, from our right to hand down our cultural heritage, and eventually from paternalistic imposition upon future generations of our irreversible choices (even eu-genetic pre-design of future persons identity).