  The pseudoforest version of the Strong Nine Dragon Tree Conjecture states
that if a graph $G$ has maximum average degree $\text{mad}(G) = 2 \max_{H
\subseteq G} \frac{e(G)}{v(G)}$ at most $2(k + \frac{d}{k+d+1})$, then it has a
decomposition into $k+1$ pseudoforests where in one pseudoforest $F$ the
components of $F$ have at most $d$ edges. This was proven in 2020. We
strengthen this theorem by showing that we can find such a decomposition where
additionally $F$ is acyclic, the diameter of the components of $F$ is at most
$2\ell + 2$, where $\ell = \lfloor\frac{d-1}{k+1} \rfloor$, and at most $2\ell
+ 1$ if $d \equiv 1 \bmod k+1$. Furthermore, for any component $K$ of $F$ and
any $z \in \mathbb N$, we have $diam(K) \leq 2z$ if $e(K) \geq d - z(k-1) + 1$.
We also show that both diameter bounds are best possible as an extension for
both the Strong Nine Dragon Tree Conjecture for pseudoforests and its original
conjecture for forests. In fact, they are still optimal even if we only enforce
$F$ to have any constant maximum degree, instead of enforcing every component
of $F$ to have at most $d$ edges.
