The cooling rate for fine glass fibers in the 6–16 &mgr; diameter range has been calculated by means of a new cooling equation. Typical strengthvsdiameter data are compared with the ratio of quenching time to the Maxwell relaxation;ts/&tgr;. Strength increases rapidly forts/&tgr; ≤ 1.0 and &tgr; is most probably of the order 10−4sec at 1100°C. The refractive index decreases slightly in the critical region but the change does not indicate a significant rise in the fictive with increased quenching. For this reason structural changes are considered of secondary importance as a factor contributing to high strength. New strength measurements of glass fibers fit a distribution law with reasonable accuracy. It is therefore concluded that the flaw theory of high strength is valid. The influence of ``hydrostatic'' cooling upon flaw generation is discussed.