Foraminiferal oxygen isotopes from deep-sea sediment cores suggest that a rapid expansion of the Antarctic ice sheet took place in the Middle Miocene around 13.9 million years ago. The origin for this transition is still not understood satisfactorily. One possible cause is a drop in the partial pressure of atmospheric carbon dioxide (pCO (sub 2) ) in combination with orbital forcing. A complication is the large uncertainty in the magnitude and timing of the reconstructed pCO (sub 2) variability and additionally the low temporal resolution of the available pCO (sub 2) records in the Middle Miocene. We used an ice sheet-climate model of reduced complexity to assess variations in Antarctic ice sheet volume induced by pCO (sub 2) and insolation forcing in the Middle Miocene. The ice-sheet sensitivity to atmospheric CO (sub 2) was tested for several scenarios with constant pCO (sub 2) forcing or a regular decrease in pCO (sub 2) . This showed that small, ephemeral ice sheets existed under relatively high atmospheric CO (sub 2) conditions (between 640-900 ppm), whereas more stable, large ice sheets occurred when pCO (sub 2) was less than approximately 600 ppm. The main result of this study is that the pCO (sub 2) -level must have declined just before or during the period of oxygen-isotope increase, thereby crossing a pCO (sub 2) glaciation threshold of around 615 ppm. After the decline, the exact timing of the Antarctic ice-sheet expansion depends also on the relative minimum in summer insolation at approximately 13.89 million years ago. Although the mechanisms described appear to be robust, the exact values of the pCO (sub 2) thresholds are likely to be model-dependent.