Is it better to soak or scrub rings?

The sequence matters because the grime that dulls a ring is mostly oil-based, and oil-based films do not respond to mechanical scrubbing until they have been softened first. A 20 to 30 minute warm soapy soak gives the surfactants in the dish soap time to break the bond between the residue and the metal or stone. After that the brush is just lifting away loosened material, not grinding through a hardened layer. Scrubbing first on a dry or only briefly wet ring wastes effort against the toughest part of the film, and the pressure needed to shift dried residue is enough to bend small prongs or loosen melee stones in pave bands.

Use a soft baby toothbrush, not a regular adult one. Adult bristles are too stiff for melee prongs and can lift settings over time. Brush from the underside of the band upward, so loosened dirt falls away from the stone rather than collecting in the prongs. Pay particular attention to the gallery between the band and the head, which catches the most residue, and to the back of the centre stone, where soap film blocks the most light. Use light pressure and rinse the brush regularly during the clean. Replace the brush every couple of months, since worn bristles fail at the same point a stiffer brush would damage the prongs.