The cardinality of a smallest set that strongly resolves every pair of vertices in $G$ is the strong dimension $\beta_s(G)$ of $G$. The threshold strong dimension $\tau_s(G)$ of $G$ is the smallest strong dimension among all graphs having $G$ as a spanning subgraph.
We show that trees with strong dimension $3$ or $4$ have threshold strong dimension $2$. Oellermann et al observed $\tau(K_{1,6}) > 2$. Since $\beta_s(K_{1,6})=5$ and $\tau(K_{1,6}) \le \tau_s(K_{1,6})$, the threshold strong dimension of trees with strong dimension $5$ need not be $2$. We observe there are trees of arbitrarily large dimension with threshold strong dimension 2.