In this work, we investigate a number of fuel assembly design options for a BWR core operating in a closed self-sustainable Th-233U fuel cycle. The designs rely on axially heterogeneous fuel assembly structure in order to improve fertile to fissile conversion ratio. One of the main assumptions of the current study was to restrict the fuel assembly geometry to a single axial fissile zone "sandwiched" between two fertile blanket zones. The main objective was to study the effect of the most important design parameters, such as dimensions of fissile and fertile zones and average void fraction, on the net breeding of 233U. The main design challenge in this respect is that the fuel breeding potential is at odds with axial power peaking and therefore limits the maximum achievable core power rating. The calculations were performed with BGCore system, which consists of MCNP code coupled with fuel depletion and thermo-hydraulic feedback modules. A single 3-dimensional fuel assembly with reflective radial boundaries was modeled applying simplified restrictions on maximum central line fuel temperature and Critical Power Ratio. It was found that axially heterogeneous fuel assembly design with single fissile zone can potentially achieve net breeding. In this case however, the achievable core power density is roughly one third of the reference BWR core.