Techniques have been developed for growing W single crystals, which demonstrate ail extremely low dislocation density and insignificant mosaic spread. The 6-8% deformation is found to be optimal to get large grains after recrystallization. The vacuum conditions are required for the crystal deformation by rolling, because they enable to avoid an oxidation of the crystal surface during deformation at high temperature. The block structure and the perfection of the crystals were controlled by the XRD technique and by anomalous transmission of the X-rays procedure. The dislocation density determined from diffraction data is close to the density values obtained from etch pits. The high-purity single crystals of low dislocation density and free of small-angle boundaries were produced. (C) 2008 Elsevier B.V. All rights reserved.