  Let ${\cal F}$ be a family of meromorphic functions on a domain $D$. We
present a quite general sufficient condition for ${\cal F}$ to be a normal
family. This criterion contains many known results as special cases. The
overall idea is that certain comparatively weak conditions on ${\cal F}$
locally lead to somewhat stronger conditions, which in turn lead to even
stronger conditions on the limit function $g$ in the famous Zalcman Lemma.
Ultimately, the defect relations for $g$ force normality of ${\cal F}$.
