Laser-induced fluorescence (LIF) measurements of nitric oxide (NO) and methylidyne (CH), previously reported for prompt-dominated laminar, counterflow, methane-air non-premixed flames at a global strain rate of 20 s(-1) and pressures from 1 to 6 atm, are analyzed by considering three important aspects of complex CH-NO kinetics. First, net reaction rates are studied as a function of pressure so as to understand the observed peaks in maximum [CH] and [NO] between 2 and 4 atm. Second, key elementary reactions are compared for two detailed chemical kinetic mechanisms, GRI 3.0 and Lindstedt, in order to investigate differences in computed [CH] and [NO]. Third, variations in rate coefficients are studied for those elementary reactions involving CH that strongly influence NO concentrations in these non-premixed flames. Rate coefficients are also considered for reaction steps which directly affect the formation and destruction of NO. On the basis of all three inquiries, rate coefficients for controlling elementary reactions are selected so as to give the best match between measured and predicted [CH] and [NO] over the investigated pressure range. In general, these analyses reveal the unique behavior of controlling elementary reactions in the intermediate pressure range of 2-4 atm. Further work on reaction dynamics is undoubtedly needed to investigate fully the highly complex chemical interactions controlling NO formation in these non-premixed flames.