A braided sleeve with complex geometry, including changes to the geometry along the braided sleeve's longitudinal axis are described. In particular, along a first portion of the braided sleeve's longitudinal axis, multiple tows are intertwined with each other. Along a second portion, one of tows is removed from being intertwined with the other tows and is relocated to an interior or an exterior of the braided sleeve. A third portion includes the removed tow being intertwined with the plurality of tows again. In this manner, the braided sleeve may provide coverage of preforms with varying diameters along the longitudinal axis of the preforms.