Spin waves in yttrium iron garnet (YIG) nano-structures attract increasing attention from the perspective of novel magnon-based data processing applications. For short wavelengths needed in small-scale devices, the group velocity is directly proportional to the spin-wave exchange stiffness constant [Formula: see text]. Using wave vector resolved Brillouin light scattering spectroscopy, we directly measure [Formula: see text] in Ga-substituted YIG thin films and show that it is about three times larger than for pure YIG. Consequently, the spin-wave group velocity overcomes the one in pure YIG for wavenumbers k > 4 rad/ μm, and the ratio between the velocities reaches a constant value of around 3.4 for all k > 20 rad/ μm. As revealed by vibrating-sample magnetometry and ferromagnetic resonance spectroscopy, Ga:YIG films with thicknesses down to 59 nm have a low Gilbert damping ([Formula: see text]), a decreased saturation magnetization [Formula: see text] mT, and a pronounced out-of-plane uniaxial anisotropy of about [Formula: see text] mT, which leads to an out-of-plane easy axis. Thus, Ga:YIG opens access to fast and isotropic spin-wave transport for all wavelengths in nano-scale systems independently of dipolar effects.