  P.Lecomte has proposed to take into account the covariant derivatives used to
build ordering prescriptions for the naturality of transformation properties
and has conjectured that there exists an natural ordering prescription for
differential operators of any orders between density bundles which in addition
is invariant under projective changes of the covariant derivatives. We prove
this conjecture by constructing a projectively invariant lift of a torsion-free
connexion to a torsion-free connexion on (the positive part of) the total space
of the bundle of all $a$-densities for nonzero $a$, by lifting the symbols in a
projectively invariant way (they turn out to be in bijection to the space of
all $\real^+$-equivariant divergence-free symmetric tensor fields on the total
space), and by using the standard ordering procedure (`all the covariant
derivatives to the right') on the total space. For Ricci-flat manifolds we show
that this ordering prescription coincides --with the appropiate replacements--
with an explicit formula in $\real^m$ obtained by Duval, Lecomte and Ovsienko.
