Consider the stationary Navier-Stokes equations in a bounded domain whose boundary consists of disjoint closed surfaces , , …, with , …, inside of . The Leray inequality of the given boundary data on plays an important role for the existence of solutions. It is known that if the flux on (: the unit outer normal to ) is zero for each , then the Leray inequality holds. We prove that if there exists a sphere in separating in such a way that , are contained in and that are in the outside of , then the Leray inequality necessarily implies that . In particular, suppose that for each each there exists a sphere in such that contains only one . Then the Leray inequality holds if and only if .