Two methods improving the brilliance of laser-induced plasmas emitting in the extreme UV (EUV) and soft x-ray (SXR) region were investigated, using three different gases (nitrogen, krypton, and xenon) from a pulsed gas jet. Utilizing a newly designed piezo electric valve, up to almost ten times higher gas pressures were applied, resulting in increased target densities and thus, higher conversion efficiencies of laser energy into EUV and SXR radiation. Secondly, geometrically reducing the angle between incoming laser beam and observed plasma emission minimizes reabsorption of the emitted short wavelength radiation. Combining both methods, the source brilliance is increased by a factor of 5 for nitrogen. Furthermore, a compact EUV focusing system for metrological applications is presented utilizing the optimized plasma source. An energy density of 1 mJ/cm² at λ = 13.5 nm in the focal spot of an ellipsoidal mirror is achieved with xenon as target gas being sufficient for material removal of PMMA samples with an ablation rate of 0.05 nm/pulse.