Computational results are reported for structures of laminar counterflow diffusion flames between carbon monoxide and air, initially at room temperature and pressure from 1 to 100 arm: with total hydrogen-atom mole fractions in the system ranging from zero to about 0.02. All strain rates considered are within a factor of ten of the critical extinction strain rate. This critical strain rate is calculated as a function of pressure and of hydrogen content and is shown to lie below measured values under most conditions. For hydrogen-free flames, activation-energy asymptotics is employed and supports the computational results. It is reasoned that trace hydrogen amounts in air and preferential hydrogen diffusion through nonplanar diffusive-thermal instability contribute to enhanced flame robustness in the experiments, while increasing buoyant convective heat loss with increasing pressure promotes extinction at the higher pressures.