Discharge based extreme-ultraviolet (EUV) sources have experienced significant progress in the last decade at different places. They are commercially available and are presently being used in scanners for EUV lithography and related development projects in the semiconductor industry. The technology has been proven to be scalable from a wavelength of 13.5 nm down to the water window spectral range (2.4 to 4.4 nm), which envisions a new generation of compact systems using soft x-rays and extreme ultraviolet (XUV) light for metrology, patterning, or microscopy. Especially for microscopy applications such as aerial imaging microscopy of EUV masks, a high brilliance is required. First results on the achievable brilliance of a gas discharge source in the XUV and soft x-ray range are presented. Currently, a brilliance of at a central wavelength of 13.5 nm and at 10.9 nm are achieved. For the 2.88-nm single emission line of nitrogen, the source produces or at a spectral bandwidth of . Based on existing data, the potential of brilliance scaling is discussed.