Latitudinal shifts in the Southern Ocean westerly wind jet could drive changes in the glacial to interglacial ocean CO2 inventory. However, whilst CMIP5 model results feature consistent future-warming jet shifts, there is considerable disagreement in deglacial-warming jet shifts. We find here that the dependence of pre-industrial (PI) to Last Glacial Maximum (LGM) jet shifts on PI jet position, or state dependency, explains less of the shifts in jet simulated by the models for the LGM compared with future-warming scenarios. State dependence is also weaker for intensity changes, compared to latitudinal shifts in the jet. Winter sea ice was considerably more extensive during the LGM. Changes in surface heat fluxes, due to this sea ice change, probably had a large impact on the jet. Models that both simulate realistically large expansions in sea ice and feature PI jets which are south of 50° S show an increase in wind speed around 55° S and can show a poleward shift in the jet between the PI and the LGM. However, models with the PI jet positioned equatorwards of around 47° S do not show this response: the sea ice edge is too far from the jet for it to respond. In models with accurately positioned PI jets, a +1° difference in the latitude of the sea ice edge tends to be associated with a −0.85° shift in the 850 hPa jet. However, it seems that around 5° of expansion of LGM sea ice is necessary to hold the jet in its PI position. Since the Gersonde et al. (2005) data support an expansion of more than 5°, this result suggests that a slight poleward shift and intensification was the most likely jet change between the PI and the LGM. Without the effect of sea ice, models simulate poleward-shifted westerlies in warming climates and equatorward-shifted westerlies in colder climates. However, the feedback of sea ice counters and reverses the equatorward trend in cooler climates so that the LGM winds were more likely to have also been shifted slightly poleward.