A method of fining low-density submerged combustion glass is disclosed. The method involves introducing unfined molten glass produced in a submerged combustion melter into a fining chamber of a downstream fining tank. Additionally, additive particles are also introduced into the fining chamber to release one or more fining agents into the molten glass bath contained in the fining chamber to accelerate the removal of bubbles from the molten glass bath. The fining of the molten glass bath as assisted by the one or more fining agents allows for fined glass to be discharged from the fining tank that has fewer bubbles and a greater density than that of the unfined molten glass introduced into the fining tank. Additive particles that include a physical mixture of a glass reactant material and the fining agent(s) are also disclosed.