  We consider the Erd\H{o}s-P\'osa property for immersions and topological
minors in tournaments. We prove that for every simple digraph $H$, $k\in
\mathbb{N}$, and tournament $T$, the following statements hold:
  $\bullet$ If in $T$ one cannot find $k$ arc-disjoint immersion copies of $H$,
then there exists a set of $\mathcal{O}_H(k^3)$ arcs that intersects all
immersion copies of $H$ in $T$.
  $\bullet$ If in $T$ one cannot find $k$ vertex-disjoint topological minor
copies of $H$, then there exists a set of $\mathcal{O}_H(k\log k)$ vertices
that intersects all topological minor copies of $H$ in $T$.
  This improves the results of Raymond [DMTCS '18], who proved similar
statements under the assumption that $H$ is strongly connected.
