The present application pertains to a compression packing seal including a braided dual-sided jacket, methods for producing and using such a seal, and apparatuses suitable for producing such a seal. The compression packing seal is made up of a core and a jacket braided round the core. The jacket may include two or more different materials that are braided together in such a way that, in cross-section, the jacket has an asymmetrical configuration relative to a first axis that is substantially perpendicular to the longitudinal axis and is substantially perpendicular to a side of the jacket. Accordingly, when viewed in a cross-sectional plane, the jacket may expose substantially only a first material along a first side, and substantially only a second material along a second side.