diff --git a/comparable-box-dimension.tex b/comparable-box-dimension.tex
index dd4877288bccb6da2c09c362aadc41b0e8c2f3ad..94bf6043b8a866fa712b50ba46292161524e5c89 100644
--- a/comparable-box-dimension.tex
+++ b/comparable-box-dimension.tex
@@ -570,6 +570,20 @@ $$|\beta(C)|-1\le (2ksd+2)^dst=f(k),$$
 as required.
 \end{proof}
 
+The proof that (generalizations of) graphs with bounded comparable box dimensions have sublinear separators in~\cite{subconvex}
+is indirect; it is established that these graphs have polynomial coloring numbers, which in turn implies they have polynomial
+expansion, which then gives sublinear separators using the algorithm of Plotkin, Rao, and Smith~\cite{plotkin}.
+The existence of sublinear separators is known to follow more directly from fractional treewidth-fragility.  Indeed, since $\text{Pr}[v\in X]\le 1/k$,
+there exists $X\subseteq V(G)$ such that $\tw(G-X)\le f(k)$ and $|X|\le |V(G)|/k$. The graph $G-X$ has a balanced separator of size
+at most $\tw(G-X)+1$, which combines with $X$ to a balanced separator of size at most $V(G)|/k+f(k)+1$ in $G$.
+Optimizing the value of $k$ (choosing it so that $V(G)|/k=f(k)$), we obtain the following corollary of Theorem~\ref{thm-twfrag}.
+
+\begin{corollary}
+For positive integers $t$, $s$, and $d$, every graph $G$
+with an $s$-comparable envelope representation in $\mathbb{R}^d$ of thickness at most $t$
+has a sublinear separator of size $O_{t,s,d}\bigl(|V(G)|^{\tfrac{d}{d+1}}\bigr).$
+\end{corollary}
+
 \subsection*{Acknowledgments}
 This research was carried out at the workshop on Geometric Graphs and Hypergraphs organized by Yelena Yuditsky and Torsten Ueckerdt
 in September 2021.  We would like to thank the organizers and all participants for creating a friendly and productive environment.