Pr-doped ${\mathrm{Lu}}_3{\left({\mathrm{Ga}}_x{\mathrm{Al}}_{1-x}\right)}_5{\mathrm{O}}_{12}:\mathrm{Pr}$ , $x=0–1$ , single crystals were grown by the micro-pulling-down method. We study luminescence and scintillation characteristics of the sample set focusing on their dependence on the gallium content. For $x=0.4$ we obtain the high figure-of-merit material with elevated density, high efficiency, and very fast scintillation response below $20\mathrm{ns}$ without any slower components. Improvement of scintillation performance is explained as due to the absence of the antisite ${\mathrm{Lu}}_{A\mathrm{l}}$ defects that was for the first time realized in such bulk garnet single crystals grown from the high temperature melt.