A detailed investigation into the dependence of the densities of the principal plasma species in the laser discharge on the buffer-gas operating parameters is reported. Simple expressions for the densities of the Cu, Br, and H species are derived by considering their major mechanisms for production and loss. These predict that the atomic Cu and Br densities are proportional to the HBr mass flow rate, whereas the density of H species (i.e., H and H2) is proportional to the added HBr partial pressure. The theory agrees well with "Hook" method measurements of Cu density in a 25-mm bore diameter device; the Cu density increases approximately in proportion to the HBr mass flow rate, whereas it depends only weakly on the HBr partial pressure. Measurements of the fraction of Cu atoms excited by the discharge pulse, the rate of regrowth of the ground-state Cu density during the inter-pulse period, and the pre-pulse plasma impedance, are also explained in accordance with the theory. The results show that the plasma conditions for maximum laser output, which are remarkably similar to those of other "halogen enhanced" Cu lasers, can be achieved more directly by adjusting the overall buffer flow rate with the partial pressure of the added HBr fixed at 1-2 mbar. The theory is also useful for predicting optimum buffer-gas conditions for a wide range of Cu HyBrID laser dimensions and operating conditions.