Very powerful volcanic eruptions cannot always form classical Plinian eruption columns 1-4. Instead, collapsing fountains may develop above the vent and shed pyroclastic flows which spread laterally along the ground 5. The upper part of these hot, dense pyroclastic flows may become buoyant through the entrainment, heating and expansion of ambient air, coupled with the sedimentation of larger clasts suspended in the flow. The buoyant material may rise, in a co-ignimbrite eruption column, carrying massive quantities of fine dust and volatiles into the stratosphere 6,7. Here we present a model of this process, and show that the co-ignimbrite columns associated with the eruptions of Toba 8,9 75,000 years ago and Tambora 10 in 1815 may have ascended only about 32 and 23 km; the latter is comparable with the less powerful 1982 Plinian eruption column of El Chichon 11. This corroborates arguments that the mass of sulphuric acid aerosols injected into the stratosphere and not the eruptive power determines the climatic impact of an eruption 12,13.