A remark concerning normal families and shared values

Abstract: We improve well-known results concerning normal families and shared values of meromorphic functions in the plane. In particular, we get as a corollary that a meromorphic function $f \colon \C \to \Cd$ that shares a non-zero finite value with $f'$, and such that $f'$ is bounded on the preimages of $f$ for a second value, is normal.