Carbon dioxide emissions per capita and income per capita are known to be very strongly related to each other. While some researchers find the relationship between the two log-linear, some others claim that the relationship between the two is log-quadratic. In a quadratic relationship, which is also known as the Environmental Kuznets Curve (EKC), the per capita carbon dioxide emissions increases with increasing per capita income, reaches a maximum, and then declines as per capita income continues to increase. Regression analyses carried out in this study with country data during 1960 to 1996 show that the relationship between per capita carbon dioxide emissions and per capita income are statistically significant not only in cases of the linear model and the EKC model, but also in case of a saturation model which is a novel feature reported for the first time in this study. For per capita incomes up to about 13,000 constant 1995 US$, the predictions of all three models are nearly the same. As the per capita income increases above 13,000 constant 1995 US$, the predictions of the three models begin to exhibit remarkably large deviations from each other. A comparative study of the three models carried out in this study shows that the saturation model, with its ever-increasing nature of per capita emissions towards a saturation value with increasing per capita income, is the one that best explains the cross-country emissions data.