A process for winding a fiber strand about a bobbin to form a wound package includes: (a) winding a fiber strand about a portion of a bobbin supported upon a rotatable collector of a winder to form a primary layer of a wound package. The primary layer has an overall length, an upper portion and a lower portion. Each of the upper portion and lower portion have a length which is less than the overall length. The primary layer has a plurality of sublayers, each of the plurality of sublayers having a plurality of layers. Each of the plurality of layers of the sublayers is successively wound upon a preceding layer and has a length which is less than the preceding layer. Each of the plurality of layers of the sublayers has an outer layer having a length which corresponds generally to the length of the lower portion, such that the primary layer is formed. A secondary layer is formed thereon which includes a plurality of layers upon the primary layer. Each of the plurality of layers is successively wound upon a preceding layer and has a length which is less than the preceding layer. The length of each of the plurality of layers has a midpoint which corresponds to a midpoint of the overall length of the primary layer, such that a wound package is formed.