A simplified model, describing the kinetic processes in a nanosecond pulsed longitudinal Ne-CuBr discharge afterglow, is made. It is shown that the influence of the active zone diameter decrease on the inversion population and hence on the output power and the laser pulse on the 248.6 nm line is due to the more effective population of the upper laser level, because of the higher neon ion density and mainly because of the more effective depopulation of the lower laser level. Optimal discharge conditions for UV laser operation are found for different active zone diameters of the laser tube - 12 mm, 9.5 mm, 9 mm, 8 mm, 5.8 mm, 5.7 mm, 5.2 mm and 4 mm. With diameter reduction a record average laser power of 1.3 W is obtained at multiline output. The highest peak pulse and average output powers are measured on the 248.6-nm laser line for the UV Cu+I lasers - 3.25 W and 0.85 W, respectively. The obtained specific average laser power is 56.6 mW.cm-3 at an active volume of 23 cm3.