The Na-Yb (or Er) co-substitution of Ca in CaNbGaO (CNGG) laser crystal is studied. In contrast to other garnets whose structural disorder is exclusively based on the presence of differently sized cations on the same crystal sites, Na incorporated in the dodecahedral site (a site also shared by Ca and trivalent lanthanides) creates diverse electric charge distributions over the dodecahedral sublattice, which adds to the disorder associated with Nb and Ga simultaneous occupation of the octahedral and tetrahedral sites. The currently determined cationic compositions of Czochralski grown congruent CNGG and Na-modified CNGG crystals show that Na incorporation reduces the cationic vacancy concentration on dodecahedral and octahedral sites but does not affect that in tetrahedral sites. Physical properties of interest for laser design (optical transmission, elastic constants, hardness, specific heat, thermal conductivity, thermal expansion, refractive index dispersion, group velocity dispersion, and thermo optic coefficients) have been systematically determined at cryogenic temperatures and above room temperature. Na incorporation into CNGG decreases the crystal growth temperature, promotes Yb doping, and importantly, increases the Yb optical bandwidth, offering good prospects for the implementation of ultrashort pulses in mode-locked laser oscillators.