  We prove the Strong Nine Dragon Tree Conjecture is true if we replace $d$
with $d + \frac{k}{2} \cdot (\big\lceil{\frac{d}{k+1}} \big\rceil - 1)
\big\lceil{\frac{d}{k+1}} \big\rceil$. More precisely: let $G$ be a graph and
let $d$ and $k$ be positive integers. If $\gamma(G) \leq k + \frac{d}{d + k +
1}$, then there is a partition into $k + 1$ forests, where in one forest every
connected component has at most $d + \frac{k}{2} \cdot
(\big\lceil{\frac{d}{k+1}} \big\rceil - 1) \big\lceil{\frac{d}{k+1}}
\big\rceil$ edges.
