Intense pulsed sources of coherent emission with a continuously tunable wavelength and a high pulse repetition frequency are necessary for atmospheric optics. The use of rhodamine lasing during pumping by a copper dye laser is the most promising. The goals of this work include using the opportunities for improving the lasing properties of dyes pumped by a copper dye laser, choosing dye mixtures that are optimum with respect to their lasing relation, and studying the influence of the dye on their lasing characteristics in order to obtain the optimum energy parameters in the device that is built using a copper vapor laser and an optical attachment. On the basis of an analysis of the equations that describe multiatomic molecular lasing, it is possible to come to a conclusion on the intermolecular processes that determine the lasing effectiveness: singlet-singlet and triplettriplet overabsorption of lasing emission, intercombination (S-T) and internal conversion, and photoconversion in excited electron states. A large probability of emission from the lower singlet state (a large value of the constant of the velocity of radiative decay) is also necessary.