  The arboricity $\Gamma(G)$ of an undirected graph $G =(V,E)$ is the minimal
number $k$ such that $E$ can be partitioned into $k$ forests on $V$.
Nash-Williams' formula states that $k = \lceil \gamma(G) \rceil$, where
$\gamma(G)$ is the maximum of $\frac{|E_{H}|}{|V_{H}|-1}$ over all subgraphs
$(V_H , E_H )$ of $G$ with $|V_H | \geq 2$. The Strong Nine Dragon Tree
Conjecture states that if $\gamma(G) \leq k + \frac{d}{d+k+1}$ for $k, d \in
\mathbb{N}$, then there is a partition of the edge set of $G$ into $k + 1$
forests on $V$ such that one forest has at most $d$ edges in each connected
component. Here we prove the Strong Nine Dragon Tree Conjecture when $d \leq
2(k +1)$, which is a new result for all $(k, d)$ such that $d > k + 1$. In
fact, we prove a stronger theorem. We prove that a weaker sparsity notion,
called $(k, d)$-sparseness, suffices to give the decomposition, under the
assumption that the graph decomposes into $k+1$ forests. This is a new result
for all $(k, d)$ where $d > 1$, and improves upon the recent resolution of the
Overfull Nine Dragon Tree Theorem for all $(k, d)$ when $d \leq 2(k +1)$. As a
corollary, we obtain that planar graphs of girth five decompose into a forest
and a forest where every component has at most four edges, and by duality, we
obtain that $5$-edge-connected planar graphs have a $\frac{4}{5}$-thin tree,
improving a result of the authors that $5$-edge-connected planar graphs have a
$\frac{5}{6}$-thin tree
