Fluorinated gas discharges are widely used by the semiconductor industry in etching and chamber cleaning applications, but the performance of these discharges varies in unpredictable ways, for unknown reasons believed to be electrical in origin. To investigate possible mechanisms for this behavior, we have measured the electrical characteristics of NF3/AT, CF4/O-2/Ar, and C2F6/O-2/Ar chamber cleaning plasmas at 6.7-267 Pa in a 13.56 MHz, capacitively coupled, parallel-plate reactor, using radio-frequency current and voltage probes and optical emission spectroscopy. From the measurements, power losses in the external circuitry surrounding the discharge were determined. Furthermore, using the measurements and equivalent circuit models, the mechanisms by which power was absorbed within the discharge itself were investigated. Power was absorbed most efficiently at particular values of the discharge impedance. These optimal impedances occur in the middle of a transition from capacitive impedances at low pressures to resistive impedances at high pressures. These results illustrate that the plasma impedance is a useful parameter fur monitoring and optimizing plasma processes in highly electronegative gases.