  Let $S$ be a compact orientable surface, and $\Mod(S)$ its mapping class
group. Then there exists a constant $M(S)$, which depends on $S$, with the
following property.
  Suppose $a,b \in \Mod(S)$ are independent (i.e., $[a^n,b^m]\not=1$ for any
$n,m \not=0$) pseudo-Anosov elements. Then for any $n,m \ge M$, the subgroup
$<a^n,b^m>$ is free of rank two, and convex-cocompact in the sense of
Farb-Mosher. In particular all non-trivial elements in $<a^n,b^m>$ are
pseudo-Anosov.
  We also show that there exists a constant $N$, which depends on $a,b$, such
that $<a^n,b^m>$ is free of rank two and convex-cocompact if $|n|+|m| \ge N$
and $nm \not=0$.
