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Yb: ZnWO4 single crystal is promising laser material. Spectroscopic studies of this crystal have shown that, along with attractive characteristics typical for tungstates of other structural classes (high specific luminescence intensities and significant inhomogeneous broadening of spectral bands), this crystal is also characterized by significant Stark splitting of the Yb3+ ground state, as well as extremely weak optical absorption in the wavelength range corresponding to the strongest luminescence band. This should facilitate the achievement of the efficient low-threshold lasing of ytterbium near 1 micron, almost insensitive to heating of the active medium during the laser operation. Undoped ZnWO4 single crystals are well known for a long time as efficient scintillating materials, and their fabrication technology is well developed. However, as our previous studies have shown, doping the crystal by Yb3+ ions without a charge compensator sharply deteriorates the crack resistance of the samples. Probably, the reason for such behavior is the formation of an increased number of cation vacancies. They serve as charge compensators for the heterovalent entrance of ytterbium into the lattice, but at the same time they should significantly worse and weaken the connection between neighboring atomic layers of the crystal structure. In the frame of our work the series of ZnWO4 single crystals doped with various concentrations of Yb3+ and Li+ ions (including zero concentrations) was grown by Czochralski. Lithium was used as a charge compensator preventing the formation of the above cation vacancies. The actual dopants concentrations in the crystals and their segregation coefficients between the crystal and the melt, were determined, as well as the unit cell parameters, the melting points, and the mechanical strength characteristics of the crystals, as a function of the dopants concentrations. It has been shown that the optimal Li+ amount in the initial charge for the crystal growth of doubled one, as compared to ytterbium amount. This results in significant enhancement of heterovalent incorporation of ytterbium with into the crystal lattice, and prevents the deterioration of crack resistance of the crystal.