A composite pipe comprises a polyetheretherketone innermost pipe around which a reinforcing overwrap is arranged. A protective sheath surrounds the overwrap. Such a composite pipe may be made by selecting a polyetheretherketone pipe having an outer region having a crystallinity of less than 25%; overlaying the selected pipe with overwrap; and subjecting the combination to heat, thereby causing the crystallinity of the outer region of the polyetheretherketone pipe to increase. The method reduces the risk of pipe failure.