The fate of heavy quarkonia states in quark-gluon plasma is encoded in the temperature
dependence of their spectral functions. Reconstruction of spectral functions from Euclidean
lattice correlators is an ill-posed problem. Despite a variety of techniques developed recently,
many questions remain unresolved. It is known that the situation may be improved using
anisotropic ensembles that provide finer resolution in the temporal direction. To date, the effort
focused on Wilson fermions. We report on our first study with anisotropic improved staggered
quarks. To compute the spectrum of the anisotropic Highly Improved Staggered Quarks (aHISQ)
we generated a library of anisotropic pure gauge ensembles. We discuss the gauge anisotropy
tuning that is performed with the Wilson and Symanzik gradient flow, as well as tuning of the
strange quark mass and quark anisotropy with aHISQ, using spectrum measurements on quenched
ensembles. Finally, we discuss the impact of anisotropy on pion taste splittings for aHISQ.