A method of of fining low-density submerged combustion glass includes introducing unfined molten glass produced in a submerged combustion melter into a fining chamber of a fining tank and, further, introducing additive particles into the fining chamber that comprise a glass reactant material and one or more fining agents. The one or more fining agents are released into the molten glass bath upon consumption of the additive particles in the molten glass bath to chemically fine the molten glass bath and the glass reactant material includes one or more materials that integrate into the molten glass bath upon melting. Additionally, the method includes discharging fined molten glass out of the fining chamber of the fining tank. The discharged fined molten glass has a volume percentage of gas bubbles that is less than the volume percentage of gas bubbles in the unfined molten glass introduced into the fining chamber.