  We characterize finite sets $S$ of nonwandering points for generic
diffeomorphisms $f$ as those which are {\em uniformly bounded}, i.e., there is
an uniform bound for small perturbations of the derivative of $f$ along the
points in $S$ up to suitable iterates. We use this result to give a $C^1$
generic characterization of the Morse-Smale diffeomorphisms related to the weak
Palis conjecture \cite{c}. Furthermore, we obtain another proof of the result
by Liao and Pliss about the finiteness of sinks and sources for star
diffeomorphisms \cite{l}, \cite{Pl}.
