We analyzed the properties of damage-resistant LiNbO3 crystals doped with Mg, Zn, or In. Damage resistance is due to an essential increase in the photoconductivity σp. In the first two compounds the increase in σp is most pronounced at concentrations exceeding certain thresholds (5.5 mol. % MgO or 7 mol. % ZnO in the congruent melt), whereas in In-doped crystals it occurs at any In concentration. The increase in σp is directly related to the reduction of the intrinsic defects NbLi because of their substitution by damage-resistant impurities. If an iron impurity is present, then an abrupt decrease in the capture cross section of Fe3+ acceptors at Mg or Zn concentrations higher than the threshold is responsible for the observed increase in σp.