  We prove that a "cushioned" Hermitian-Einstein-type equation proposed by
Demailly in an approach towards a conjecture of Griffiths on the existence of a
Griffiths positively curved metric on a Hartshorne ample vector bundle, has an
essentially unique solution when the bundle is stable. This result indicates
that the proposed approach must be modified in order to attack the
aforementioned conjecture of Griffiths.
