To improve the far-field directivity properties of a given mid-range acoustic horn, previously designed by shape optimization to exhibit almost ideal transmission properties in the frequency range 1.6–9.05 kHz, we apply layout optimization of thin sound-hard material in the interior of the horn. The purpose of the optimization is to place scattering material to prevent the sound intensity to increasingly be concentrated, with increasing frequency, along the horn axis. Absence or presence of thin sound-hard material is modeled by an equivalent surface transmission impedance, and the optimization algorithm determines the distribution of air or sound-hard material along a “ground structure” in the form of a grid inside the horn. The surface impedance is numerically handled using a newly developed finite-element formulation that allows exact enforcement of a vanishing impedance, corresponding to air, which would not be possible using a standard formulation. Horns provided with the optimized scatterers show a much improved angular coverage, compared to the initial configuration, with beam widths that exceed 60 ∘ uniformly over the operational frequency range, without destroying the good transmission properties of the initial horn.