The meridional circulation of the stratosphere, or Brewer‐Dobson circulation (BDC), is projected to accelerate with increasing greenhouse gas (GHG) concentrations. The acceleration is typically quantified by changes in the tropical upward mass flux (F_trop) across a given pressure surface. Simultaneously, models project a lifting of the entire atmospheric circulation in response to GHGs; notably, the tropopause rises about a kilometer over this century. In this study, it is shown that most of the BDC trend is associated with the rise in the circulation. Using a chemistry‐climate model (CCM), F_trop trends across 100 hPa are contrasted with those across the tropopause: while F_trop at 100 hPa increases 1–2 %/decade, the mass flux entering the atmosphere above the tropopause actually decreases. Similar results are found for other CCMs, suggesting that changes in the BDC may better be described as an upward shift of the circulation, as opposed to an increase, with implications for the mechanism and stratosphere‐troposphere exchange.