  We prove that for any positive integers $k$ and $d$, if a graph $G$ has
maximum average degree at most $2k + \frac{2d}{d+k+1}$, then $G$ decomposes
into $k+1$ pseudoforests $C_{1},\ldots,C_{k+1}$ such that there is an $i$ such
that for every connected component $C$ of $C_{i}$, we have that $e(C) \leq d$.
