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Vertical directional strength is significantly weaker than planar directional strength in polymer extrusion additive manufacturing due to its layer-wise deposition method. The disparity between the planar strength and vertical strength is even larger for a printed part with a fiber-reinforced thermoplastic. A printing technique has been proposed in which continuous material is extruded across layers throughout the body of the part in order to improve the strength in the vertical direction. The mechanical engagement between the material extruded in vertically aligned holes (called "z-pins") and the surrounding layers is primarily influenced by the geometry of the hole and the extrusion volume of the z-pin. Previously, the z-pinning parameters that provide good penetration in the hole has been evaluated for neat polylactic acid (PLA). The current study investigates z-pinning parameters for carbon fiber-reinforced PLA as a function of the quality of mechanical engagement of the pins with the surrounding structure. The results of this parametric 2 study will provide guidance for general printing applications across multiple platforms with various materials.