Optical cooling in Yb-doped silica fibers using anti-Stokes fluorescence has become a subject of great interest in the fiber laser community. This paper provides an update on the development of silica fibers designed specifically to enhance their cooling properties. This growing list includes a new, nearly single-mode fiber with a borophosphosilicate core that produced –65 mK of cooling with only 260 mW of 1040-nm pump power. The silica compositions that have now been successfully cooled at atmospheric pressure by anti-Stokes fluorescence by our team include aluminosilicate, aluminofluorosilicate, borophosphosilicate, and aluminosilicate doped with one of three different alkali-earth nanoparticles (Ba, Sr, and Ca). By fitting the measured temperature dependence of the cooled fiber on pump power, two key parameters that control the degree of cooling are inferred, namely the critical quenching concentration and the absorptive loss due to impurities. The inferred values compiled for the fibers that cooled indicate that the extracted heat is highest when the Yb concentration is 2 wt.% or more (to maximize heat extraction), the Al concentration is ~0.8 wt.% or greater (to reduce quenching), and the absorptive loss is below approximately 15 dB/km, and ideally below 5 dB/km (to minimize heating due to pump absorption). Only two of the reported fibers, an LaF3-doped and an LuF3-doped nanoparticle fiber, did not cool, because their Yb and Al concentrations were not sufficiently high. This analysis shows that through careful composition control (especially the Al and Yb concentrations) and minimization of the OH contamination, a new generation of Yb-doped silica fibers is emerging with higher Yb concentrations, greater resistance to quenching, and lower residual loss than commercial Yb-doped fibers. They can be expected to have a significant impact not only on optically cooled devices but also on a much broader range of fiber lasers and amplifiers.