A method of filling a canister with vitrified waste starting with a waste, such as high-level radioactive waste, that is cooler than its melting point. Waste is added incrementally to a canister forming a column of waste capable of being separated into an upper zone and a lower zone. The minimum height of the column is defined such that the waste in the lower zone can be dried and melted while maintaining the waste in the upper zone below its melting point. The maximum height of the column is such that the upper zone remains porous enough to permit evolved gases from the lower zone to flow through the upper zone and out of the canister. Heat is applied to the waste in the lower zone to first dry then to raise and maintain its temperature to a target temperature above the melting point of the waste. Then the heat is applied to a new lower zone above the melted waste and the process of adding, drying and melting the waste continues upward in the canister until the entire canister is filled and the entire contents are melted and maintained at the target temperature for the desired period. Cooling of the melted waste takes place incrementally from the bottom of the canister to the top, or across the entire canister surface area, forming a vitrified product.