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A laser model was developed to predict the performance of optically pumped higher overtone molecular lasers under pulsed and continuous wave (CW) excitations. This model takes into account up to 30 rotational levels in each of the eight vibrational states considered. Collision-induced relaxation among rotational levels, vibrational levels, energy transfer to translational degrees of freedom, and interactions with buffer gas, and the temperature dependence of these processes are included. Using parameters for a second overtone pulse pumped HBr laser, a complete lasing cascade can be expected at a certain pump pulse fluence resulting in maximum achievable efficiencies approaching 80%. Optimum operational pressure and temperature conditions are determined by the gas kinetic rates and line broadening effects. Frequency tuning and spectral narrowing of the laser output is possible with the insertion of intracavity filters without sacrificing laser output power owing to efficient energy redistribution between rotational levels mediated by appropriate buffer gases. CW lasing using waveguide (WG) like geometries is possible with efficiencies approaching 92% for first overtone pumped lasers. Heat conduction through the active gas enhanced by buffer gases and subsequent heat dissipation through the cooled WG walls are expected to handle the thermal load up to kW output power levels.