A process for making a paper product comprising: providing a forming fabric; causing the forming fabric to rotate such that an upper surface of the forming fabric moves in a machine direction; providing a multi-layer headbox comprising first and second inlet headers and a slice outlet; providing a first aqueous slurry of first fibers to the first inlet header and a second aqueous slurry of second fibers to the second inlet header; combining streams of the first and second aqueous slurries to define a jet exiting the slice outlet; emitting the jet onto the upper surface of the forming fabric to form a web; causing the forming fabric to oscillate in a direction transverse to the machine direction, whereby at least a significant number of the first fibers are caused to align in a direction that deviates from the machine direction; and forming the paper product from the web.