  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.
