Based on the kinetic process of UV Cu+ laser in longitudinal nanosecond-pulsed discharge, the necessary condition for the population inversion between the upper and lower laser levels has been obtained. The experimental phenomenon that the laser power increases rapidly with the decrease of the discharge tube aperture has been analyzed theoretically. It is pointed out that the radiation trapping of lower laser level could be restrained effectively by reducing the tube radius, resulting in the increase of depopulation rate of lower laser level and the laser power.