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Predictions for sea-level rise this century due to melt from Antarctica range from zero to more than one metre. The highest predictions are driven by the controversial marine ice-cliff instability (MICI) hypothesis, which assumes that coastal ice cliffs can rapidly collapse after ice shelves disintegrate, as a result of surface and sub-shelf melting caused by global warming. But MICI has not been observed in the modern era and it remains unclear whether it is required to reproduce sea-level variations in the geological past. Here we quantify ice-sheet modelling uncertainties for the original MICI study and show that the probability distributions are skewed towards lower values (under very high greenhouse gas concentrations, the most likely value is 45 centimetres). However, MICI is not required to reproduce sea-level changes due to Antarctic ice loss in the mid-Pliocene epoch, the last interglacial period or 1992-2017; without it we find that the projections agree with previous studies (all 95th percentiles are less than 43 centimetres). We conclude that previous interpretations of these MICI projections over-estimate sea-level rise this century; because the MICI hypothesis is not well constrained, confidence in projections with MICI would require a greater range of observationally constrained models of ice-shelf vulnerability and ice-cliff collapse.