For $\Gamma = \Sigma_{2n+3}(J_2(\mathbb{R}))$, we show there is no sequence of distinct sets in $\Gamma$ of length $\delta_\Gamma$. Our proof builds on the analysis of the mice $M_n^{ld}$ performed by Rudominer, Steel, and Woodin. This is joint work with Itay Neeman.