If B is a p-block of a group G with a cyclic defect group D, the structure of the block B (in particular the decomposition matrix) can be determined, though the proofs are quite difficult for an arbitrary finite group G. In this talk, we will see that there is a much easier approach if the group is assumed to be p-solvable, using only the Fong-Swan theorem and very basic facts about solvable groups and their characters. Since this approach essentially uses only characters, we will see that some it can be generalized to irreducible pi-partial characters of pi-separable groups. (This is joint work with Mark Lewis.)