In these proceedings, three recent results on charm strong-phase measurements from BESIII are presented. These are necessary external inputs to model-independent measurements of the CKM angle $\gamma$. Furthermore, they can also be used in studies of $D^0$-$\bar{D^0}$ mixing and $C\!P$-violation measurements. First, the strong-phase difference in the decay $D\to K^-\pi^+$ is presented, and it is the most precise determination using quantum-correlated decays. Second, the decay mode $D\to K^-\pi^+\pi^-\pi^+$ has been analysed with a phase-space binned strategy, using a binning scheme optimised for sensitivity to $\gamma$. Finally, the first measurement of the $C\!P$-even fraction of $D^0\to K^+K^-\pi^+\pi^-$ is discussed.