A commutative ring R is said to be a phi-ring if its nilradical Nil(R) is both prime and comparable with each principal ideal. The name is derived from the natural map phi from the total quotient ring T(R) to R localized at Nil(R). An ideal I that properly contains Nil(R) is phi-divisorial if (phi(R): (phi(R):phi(I)))=phi(I). A ring is a phi-Mori ring if it is a phi-ring that satisfies the ascending chain condition on phi-divisorial ideals. Many of the properties and characterizations of Mori domains can be extended to phi-Mori rings, but some cannot.