Operation of copper vapor lasers (CVL's) using on-axis unstable resonators with very high magnifications M is characterized. A single medium-scale device (1-m-long, 25-mm-diameter bore) with M = 360 is capable of delivering 10 W of high-beam-quality (HBQ) output with a divergence of less than two times the diffraction limit at a wall-plug efficiency of 0.5%. The enhanced performance is achieved by tailoring the radial profiles of the initial amplified spontaneous emission (ASE) seed and gain, by means of varying the total neon buffer gas pressure, the partial hydrogen (H 2) content of the buffer gas, and power loading of the laser head. The degree of insulation of the plasma tube is found to be an important design criterium for optimizing the HBQ performance. These results indicate that efficient generation of HBQ output from medium-scale CVL's requires both a high degree of thermal insulation and operation at high buffer gas pressures with ambient H 2 concentrations of the order of 1%.