This paper presents, for the first time to the best of our knowledge, the linewidth, frequency, and stability characteristics of a copper-HBr laser. These spectral purity attributes were found to be critically linked with the electrical input power and HBr concentration, unlike that of the optical resonator. Variation in green and yellow radiation linewidths from 4 to 4.5 GHz and from 6.5 to 8.8 GHz, linewidth fluctuations from 50 to 150 MHz and from 60 to 530 MHz as well as frequency fluctuations from 10 to 100 MHz and from 410 to 10 MHz were observed when varying the input power and HBr concentration. These results are comprehensively analyzed in terms of isotopic shift, hyperfine splitting, line broadening, and temperature and gain distribution effects relevant to this laser.