Superequilibrium concentrations of oxygen atoms which enhance the production of prompt NO in laminar premixed methane-air flames are usually computed using elaborate flame codes. This paper presents a simple method to compute superequilibrium O atom concentrations and simplifies the prompt NO mechanism using steady state relationships such that the flamefront NO production depends solely on the rates of just 3 reactions. The results show that the contribution of the N2O mechanism to the total NO increases dramatically with pressure and that the Fenimore mechanism is more important than the Zeldovich and N2O pathways in the cooler regions of the flame.