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X-ray spectral characteristics of a vacuum discharge plasma with the storage energy lower than 30 J initiated on an Al or a Fe cathode by a 1012 W/cm2 neodymium laser were studied in the 30 – 300 Å wavelength range. It is shown that both the spectral composition and intensity of radiation of a micropinch plasma produced in the cathode jet of the discharge are determined by parameters of the discharge and laser pulse. These parameters were optimized to achieve a regime in which a considerable part of radiation energy was concentrated in the long-wavelength band of the quasi-continuum (230 - 270 Å and 160 - 200 Å for Al and Fe, respectively), which makes this discharge a source of narrowband X-ray radiation.