A parametric study of the output power of supersonic chemical oxygen-iodine lasers (COILs) is carried out, applying a kinetic-fluid dynamics model calculations as well as an analytical model and comparing the results to experimental studies. The I2 dissociation mechanism recently suggested by Azyazov [J. Chem. Phys. 130, 104306 (2009)], which was previously used for comparison of model calculations to measurements of the small signal gain [K. Waichman, J. Appl. Phys. 106, 063108 (2009)], is applied here for a similar, but more sensitive, comparison of the laser output power. The dependence of the power on iodine flow rate and on mirror transmission is studied for low and high pressure COILs, respectively. Good agreement between the calculated and measured power is obtained for both low and high pressure COILs only when the processes suggested by Azyazov are included in the calculations. This is different from the situation for the gain where for high pressure COILs, the calculated values were insensitive to the assumed dissociation mechanism, although for low pressure the measurements were reproduced only by applying the Azyazov mechanism. We believe that the results of the present work strongly support the application of this mechanism for modeling the COIL operation.