The nonlinear relationship between luminance and DAC count could be characterized with the simplified model, if optimum brightness level is set. In this study, we propose a technique to set the optimum level of brightness, in which offsets for RGB channels can be assumed to zero, and determine the gamma coefficients from log-log data without nonlinear optimization. The optimum brightness level could be found by measuring a few tones of neutral for the combination of 3 levels of brightness and 2 levels of contrast. This technique has two advantages, it does not require measurements for 0 DAC count, and does not require nonlinear optimization in finding the gamma coefficient of the display system. Two CRT monitors by different manufacturers have been rested. As the result, all monitors could be set to their optimum state with a different combination of brightness and contrast. In that state, the gamma coefficient for each channel could be determined from two measuring data and the tone reproduction characteristics of the RGB channel could be characterized with the simplified equation, neglecting offset and gain. The accuracy of characterization was better than 0.5 Delta E*(ab) for 125 colors for a monitor having good channel independence.