Room Treatment for high frequencies

Generally hard, materials with small size placed in front of absorbers will maintain high fregs that way that:

frequencies with lambda < 2x size are mostly reflected
frequencies with lambda > 2x size are mostly absorbed (shunning reflective object)

frequencies in the cross over range in between 0,5 ... 2x size do both and are subject of bending and interference issues

A good practice for small rooms is to put absorbers aside to the walls in an appropriate angle to reflect to the rear wall and cover these absorbers with wooden bars upright at different widths and distance.
 
One has to make sure that small particles (in case of rock wool, or glas wool, fibre) does not inflitrate the air. Many people cover these with a foil, which must be very thick if it is to carry anything overhead and thus reflect itself. Unfortunately, foils have a very unsightly reflection spectrum, which is why this must be covered again with acoustically absorbent material. This means that the highest trebles are gone again.😱

On the other hand, absorbers with somewhat stiffer properties reflect the waves incident obliquely from the side more than they absorb them, so the highs from the speakers are quite preserved in some overhead arrangements.🙂
 
Closer on tweeter axis is main listening position

I set up a listening position in an untreated room. the room opens into adjacent room. The chair is placed in the opening to adjacent room. The speakers are placed so partial walls on L/R reflect back toward speakers away from listening chair. There's a lowered ceiling area that also reflect back toward speakers.. The speakers are about 2m distance. This setup is creates a direct well focused sound with nothing spent on acoustic treatment.. The opening also smooths bass response.