Let w be a pseudo-valuation
defined on a commutative ring R and let S be an overring of R. This paper
investigates conditions needed to imply that w can be extended to S. These
conditions are given in terms of a particular sequence of ideals {Ai}i=0∞ in R which
is called the best filtration for w. The main theorem states that if w is a
pseudo-valuation on R with best filtration {Ai} and each Ai is a contracted ideal
with respect to S, then w can be extended to S. The converse of this result is then
proved.