This paper quantifies the role of changing sea level in affecting Mediterranean stratification using a new model of the strait-basin system, which allows for explicit time dependence. During the last deglaciation, Fairbank's Meltwater Peak 1B leads to rapidly rising global sea levels and a freshening of the oceans and hence increasing influx of ever freshening Atlantic water into the Mediterranean basin. Owing to long residence times, the salinity of the deep and intermediate water reservoirs would have decreased more slowly, so that the basin was more stably stratified for a period, with possible implications for sapropel formation. Our model is used to estimate the size of this reservoir effect in comparison to the freshwater influx from the opening of the Black Sea at the Bosphorus. It is found that this mechanism affects the stratification to a similar degree as the Black Sea opening. Other climatic mechanisms have also affected the freshwater budget of the Mediterranean at this time, but their sizes are more difficult to quantify.