Synchrotron-based full-field tomographic microscopy established itself as a tool for noninvasive investigations. Many beamlines worldwide routinely achieve micrometer spatial resolution while the isotropic 100-nm barrier is reached and trespassed only by few instruments, mainly in the soft x-ray regime. We present an x-ray, full-field microscope with tomographic capabilities operating at 10 keV and with a 3D isotropic resolution of 144 nm recently installed at the TOMCAT beamline of the Swiss Light Source. Custom optical components, including a beam-shaping condenser and phase-shifting dot arrays, were used to obtain an ideal, aperture-matched sample illumination and very sensitive phase-contrast imaging. The instrument has been successfully used for the nondestructive, volumetric investigation of single, unstained cells.