This paper documents two methods of improving the performance of volume-to-point tree networks for two-dimensional heat conduction. These improvements are offered relative to the design produced by the constructal method, in which optimized volume elements (building blocks) are presented and grouped into larger constructs, which are also optimized. The first improvement is that each construct is optimized with respect to all its degrees of freedom: unlike in the constructal method, the optimized features of the smaller building blocks are not preserved during the optimization of the construct. The second improvement opportunity is that spacings are allowed between the facing tips of neighboring high-conductivity inserts. All such spacings are optimized. Another new direction pursued in this paper is the optimization of tree networks that must fill a volume with prescribed external shape (e.g., square, or disk). The designs optimized numerically in this paper lower the volume-to-point resistance beyond the levels achieved based on the constructal method, and bring the shape of the conduction tree closer to the shapes seen in nature.