As the life time of the vibrational modes (001) and (100) of CO2 are different, the population inversion in gasdynamic laser (GDL) is sensitive to the cooling rate of gas. If the cooling rate of gas is too fast, both levels will stay hot and so the gain decreases. However, if the cooling rate is too slow, two lasing levels cool down accordingly and again it lowers the gain. In turn, the slope of the supersonic nozzle affects the cooling rate of the levels and also the population inversion. Thus, the shape of a supersonic nozzle is an important factor in small signal gain of CO2 gasdynamic laser. On the basis of mean value theorem, one would expect that for every family of supersonic nozzle shapes (shock free, wedged, logarithmic, and exponential), there will be a specific one having an optimum cooling and gain. Small signal gain of a GDL was calculated for the different nozzle shape of the different families. It was found that the exponential nozzle shapes would give an optimum population inversion.