The invention relates to a method of producing a preform for a holey optical fiber, and more particularly, to a method of producing polymer holey optical fiber using novel capillary and cane designs that allow a construction of complex holey structures. The capillaries may have a complex internal structure including multiple holes, holes of non-circular shape, off-center holes, holes of different sizes, or any combination of these. The canes may have a complex external shape to define interstitial holes when the canes arc combined in a stack (see FIG. 1). The capillaries and canes may be made of different materials and combined within the same structure.