This study revisits how critical thresholds for tipping of the Atlantic Meridional Overturning Circulation (AMOC) are derived from comprehensive climate models. It is shown that the method for keeping the global salinity constant – by compensating salinity either at the surface or throughout the ocean volume – matters for AMOC tipping: with surface compensation, the tipping point shifts to larger freshwater forcing values, mainly due to (artificial) salt input in the North Atlantic and Arctic.