Joint work with Ari Meir Brodsky.

**Abstract.** Schimmerling asked whether $\square^*_\lambda$ together with GCH entails the existence of a $\lambda^+$-Souslin tree, for a singular cardinal $\lambda$. Here, we provide an affirmative answer under the additional assumption that there exists a non-reflecting stationary subset of $E^{\lambda^+}_{\neq cf(\lambda)}$.

As a bonus, the outcome $\lambda^+$-Souslin tree is moreover *free*.

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