A small-bore diffusion relaxed N2-laser (P<200 Torr) with longitudinal and transverse excitation in single- and multichannel discharge configurations is developed. We show that the maximum repetition rate and specific average power of the laser are increased with the decrease of the characteristic transverse dimension of the discharge channel. An 8-kHz repetition rate and average power of 6.4 mW are obtained in very compact laser structures. A specific average power of about 160 mW/cm3 is achieved, that is a few times higher than that extracted from largebore plasma tubes. The laser with transverse excitation produces 30-kW pulses at 500 Hz. The waveguide effect in the laser channel and its influence on the spatial distribution and coherence of the laser radiation are also studied.