  In this paper, we prove a quantitative version of the Tits alternative for
negatively pinched manifolds $X$. Precisely, we prove that a nonelementary
discrete isometry subgroup of $\mathrm{Isom}(X)$ generated by two non-elliptic
isometries $g$, $f$ contains a free subgroup of rank $2$ generated by
isometries $f^N , h$ of uniformly bounded word length. Furthermore, we show
that this free subgroup is convex-cocompact when $f$ is hyperbolic.
