  Given a rational dominant map $\phi: Y \dashrightarrow X$ between two generic
hypersurfaces $Y,X \subset \mathbb{P}^n$ of dimension $\ge 3$, we prove (under
an addition assumption on $\phi$) a "Noether-Fano type" inequality $m_Y \ge
m_X$ for certain (effectively computed) numerical invariants of $Y$ and $X$.
