A method of making optical fibers that includes controlled cooling to produce fibers having a low concentration of non-bridging oxygen defects and low sensitivity to hydrogen. The method may include heating a fiber preform above its softening point, drawing a fiber from the heated preform and passing the fiber through two treatment stages. The fiber may enter the first treatment stage at a temperature between 1500° C. and 1700° C., may exit the first treatment stage at a temperature between 1200° C. and 1400° C., and may experience a cooling rate less than 5000° C./s in the first treatment stage. The fiber may enter the second treatment stage downstream from the first treatment stage at a temperature between 1200° C. and 1400° C., may exit the second treatment stage at a temperature between 1000° C. and 1150° C., and may experience a cooling rate between 5000° C./s and 12,000° C./s in the second treatment stage. The method may also include redirecting the fiber with a fluid bearing device or an air-turn device.