Let $g(t)$ be a compact Ricci flow on $[0,T)$ with a Type I singularity, let $p\in M$, let $t_j\uparrow T$, and set $\lambda_j=(T-t_j)^{-1}$. If the pointed rescaled flows
based at $p$ subconverge smoothly in the pointed Cheeger-Gromov sense on compact time intervals $s\in(-\infty,0)$, then every nonflat limit is an ancient gradient shrinking Ricci soliton.