Sudden stratospheric warming (SSW) events have been suggested to be followed by a surface impact, though this response varies between events. Using reanalysis data, we identify two types of tropospheric responses to SSWs: Two thirds of the SSW events are dominated by a zonally symmetric tropospheric response with an equatorward shift of the jet in the Atlantic, consistent with the canonical SSW response in the form of a negative signature of the North Atlantic Oscillation. For the remaining third of SSW events, a zonally asymmetric response is found, associated with a poleward shift of the jet in the Atlantic. The Pacific is found to contribute to the sign of the North Atlantic response, as synoptic wave propagation from the Eastern Pacific links the Pacific and Atlantic storm tracks for both equatorward and poleward jet responses.