Previously we have proposed a simple zerotree coding algorithm called Listless Zerotree Coding (LZC) that has a significantly lower coding memory requirement than SPIHT. However, LZC performs the SPIHT-like recursive tree search that produces reconstructed images of uneven visual quality at low bit-rates. Therefore, in this paper we propose a new LZC algorithm called Tree-Pruning Listless Zerotree Coding (TPLZC) that performs a raster tree search for a better reconstructed image quality. Nevertheless, the zerotree relation is no longer embedded in the raster tree search, so additional buffer memory will be required to store the matrix-wide zerotree relations. TPLZC utilizes a simple tree-pruning method and a flag bit-map to construct and store the entire zerotree structure. As a result, TPLZC exhibits not only a low coding memory requirement but also a low coding complexity.