Strand guide eye and method of winding a package using the same

A guide eye for use with a traverse mechanism of a strand package winder is positioned with respect to the surface of the package during the package build process so that the guide eye contacts the package surface in the larger diameter, end regions of the package. This positioning provides a minimal free length between the point at which the strands leaves the guide and the point at which the strand contacts the package surface, giving better control over the placement of the strand onto the package surface, particularly in the end portions of the package. Further, the guide eye is pressed against the package surface, slightly compressing the surface and pressing a portion of the preceding stand courses against the package. This pressure helps to fix the strand in the position in which it was laid down to reduce displacement of the strand course during the package build process.