Iff= (In)n≥1 is filtration on a commutative ringRandEis anR-module, then a filtratione= (En)n≥1 onEis calledf-good in caseImIn⊂Em+nfor allm≥1 andn≥ 1 and there exists a positive integermsuch thatfor all n >m (This is an extension of the usual definition of e beingi-good withian ideal inR) A number of the basic results concerned withR-good filtrations are extended tof-good filtrations, and it is then shown that iff= (In)n≥1 andk= (Kn)n ≥1 are regular filtrations onRsuch thatKn⊆Infor all n ≥ 1, and ifkisf-good, then the complete integral closures of the Rees rings offandkare equal.