Let A be a commutative ring. The concept of a reduction I of an ideal J of A which was introduced in [6] has been extended recently in many ways to a pair (f,g) of filtrations on A, where f <g. It has given rise to the concept of an f-good (resp. f-fine) filtration in [9] and to that of an integral (resp. a strongly integral) filtration over f in [33 and also to the concept of a reduction of g in [7]. Here we introduce a new concept of a reduction of the filtration g which is closer to that ofan ideal and we study the relationship with the above concepts. For any filtration f = (In) on A consider