Rate equations are developed and used to calculate the monochromatic laser power densities (~100 kw cm 2 ) that are required to effectively saturate the excited atom population in typical hot gases (<3000°K) such as flames used for analytical atomic resonance fluorescence. Results are briefly compared with characteristics of present day lasers. A nearly-saturated population provides greater regulation of the fluorescent emission with respect to changes in laser power density and quenching. The proportionally greater laser energy needed degrades detection limits when scattering is a major contributor to noise.