A method of fining glass is disclosed that includes flowing a molten glass bath through a fining chamber. The molten glass bath has an undercurrent that flows beneath a skimmer that is partially submerged in the molten glass bath. One or more fining agents are introduced into the undercurrent of the molten glass bath directly beneath the skimmer from a carrier gas. In this way, the fining agent(s) may selectively target the gas bubbles drawn under the skimmer within the undercurrent of the molten glass for removal. The method may be employed to fine molten gas produced in a submerged combustion melter. A fining vessel for fining molten glass is also disclosed.