Improved polybenzoxazole fibers are made by a process for finishing a spun and drawn dope fiber, which contains polybenzoxazole polymer and a solvent acid, comprising the steps of: (a) coagulating the dope fiber in an aqueous coagulant; (b) washing the coagulated fiber with an aqueous washing fluid for less than 72 hours under conditions such that the fiber contains no more than 8,000 ppm residual solvent acid (1 ppm = 1 part per million, by weight); (c) drying the fiber at a temperature of 120 °C to 300 °C until it retains no more than 2 weight percent residual moisture; and (d) heat-treating the fiber at a temperature of at least 300 °C under tension.