Nielsen methods and groups acting on hyperbolic spaces
  We show that for any positive integer $n$ there exists a constant $C(n)>0$ such that any $n$-generated group $G$, which acts by isometries on a $\delta$-hyperbolic space (with $\delta>0$), is either free or has a nontrivial element with translation length at most $\delta C(n)$. 
Ilya Kapovich and Richard Weidmann