We present the design of realistic annular photonic-crystal (APC) structures of finite thickness aiming to obtain a complete photonic bandgap (PBG). The APC is composed of dielectric rods and circular air holes in a triangular lattice such that each rod is centered within each hole. The optical and geometrical values of the structure are studied, and the interplay between various design parameters is highlighted. The coupled role of the inner-dielectric-rod radius, material types, and slab thickness is investigated. It is shown that the slab thickness is vital to obtain a complete photonic bandgap below the light line, and the specific value of the inner-dielectric-rod radius to sustain the maximum PBG if the hole radius is fixed at proper value is found. (C) 2008 Optical Society of America.