An optical fiber comprising a multimode glass core having a diameter of at least 250 microns and an index of refraction and a polymer cladding having a thickness and contactingly surrounding a glass portion of the fiber so as to define an interface between the glass portion and the polymer cladding. The polymer cladding can have a first index of refraction that is less than the index of refraction. The fiber can comprise a density of less than 0.25 non-conforming regions having a diameter of 25 microns or greater per millimeter of length along the fiber, where each of the non-conforming regions is a region visible to the human eye under an optical microscope and having at least a portion thereof within a selected distance of the interface. The selected distance can be less than or equal to the thickness of the polymer cladding. The optical microscope can have a total magnification of about 200. The polymer cladding can be applied to at least a part of the optical fiber in at least a class 1000 environment. Methods of using optical fibers, including receiving with an optical fiber optical energy from a source and guiding the optical energy with the optical fiber, wherein the optical energy comprises at least one of 1) pulses each comprising a peak power of at least 10 kW, 2) an average power of at least 50 Watts, or 3) an average power density of at least 2.9 kW/cm.sup.2.