A non-return valve having an accumulation damper movable relative to a housing and shaped like a bowl to accumulate condensate running down from the chimney. The non-return valve has a smaller floating damper made of a material having a density less than water for resting against the accumulation damper when the appliance is in standstill and sealing the drainage holes in the accumulation damper when the condensate accumulation is below a threshold. Once condensate accumulates in the accumulation damper beyond the threshold, the floating damper is buoyed by the condensate thereby breaking the seal with the drainage holes and permitting the condensate to drain through drainage holes in the accumulation damper. When the appliance is operational, exhaust from the appliance lifts the floating damper and, in some cases, the accumulation damper also, to permit exhaust of combustion gases up the chimney.