  A digraph is {\it $n$-unavoidable} if it is contained in every tournament of
order $n$. We first prove that every arborescence of order $n$ with $k$ leaves
is $(n+k-1)$-unavoidable. We then prove that every oriented tree of order $n$
($n\geq 2$) with $k$ leaves is $(\frac{3}{2}n+\frac{3}{2}k -2)$-unavoidable and
$(\frac{9}{2}n -\frac{5}{2}k -\frac{9}{2})$-unavoidable, and thus
$(\frac{21}{8} n- \frac{47}{16})$-unavoidable. Finally, we prove that every
oriented tree of order $n$ with $k$ leaves is $(n+ 144k^2 - 280k +
124)$-unavoidable.
