  Berkovich, Chillag and Herzog characterized all finite groups $G$ in which
all the nonlinear irreducible characters of $G$ have distinct degrees. In this
paper we extend this result showing that a similar characterization holds for
all finite solvable groups $G$ that contain a normal subgroup $N$, such that
all the irreducible characters of $G$ that do not contain $N$ in their kernel
have distinct degrees.
