It has been demonstrated that distillation profiles can be employed
to build optimized quarkonium interpolators for spectroscopy calculations
in lattice QCD. We test their usefulness for heavy-light systems on
(3+1)-flavor ensembles with mass-degenerate light and a charm quark in
the sea in preparation for a future $D\bar{D}$-scattering analysis.
The additional cost of light inversions naturally leads to the question
if knowledge of optimal profiles can be used to avoid superfluous
computations. We show such optimal profiles for different lattice sizes and pion masses and discuss general
trends.
Furthermore, we discuss the handling of momenta in this framework.