Observations reveal that the substantial cooling of the global lower stratosphere over 1979-2003 occurred in two pronounced steplike transitions. These arose in the aftermath of two major volcanic eruptions, with each cooling transition being followed by a period of relatively steady temperatures. Climate model simulations indicate that the space-time structure of the observed cooling is largely attributable to the combined effect of changes in both anthropogenic factors (ozone depletion and increases in well-mixed greenhouse gases) and natural factors (solar irradiance variation and volcanic aerosols). The anthropogenic factors drove the overall cooling during the period, and the natural ones modulated the evolution of the cooling.