The spectrum of static-light and static-charm mesons is studied using optimized distillation in two different $N_{\rm{f}} = 3 + 1$ QCD ensembles with pion masses of $m_{\pi} \approx 800 \, \text{MeV}$ and $m_{\pi} \approx 420 \,\text{MeV}$ and a heavy (charm) quark. Local and derivative-based operators are used to access states of multiple quantum numbers. The use of optimal profiles is shown to improve the overlap with the energy states compared to standard distillation.