If you want the wheel actually clean, yes. Most of the brake dust sits on the inner barrel where a mitt cannot reach, and a wheel that looks clean from the front while the inside is still black is the most common thing we see. A long soft barrel brush plus a smaller one for the face covers nearly every wheel.

Old dressing and blooming agents still in the rubber. Scrub the tyre back with a tyre cleaner or an APC and a stiff brush until the foam runs clean, then dress it. Dressing over dirt is what browns a week later.