SPIHT algorithm is a wavelet based fast and effective technique for image compression. It uses a list structure to store status information which is generated during set-partitioning of toro-tree. Usually, this requires lots of additional memory depending on how high the bit-rate is. Therefore, in this paper, we propose a new technique called MZC-BFS, which needs no additional memory when running SPIHT algorithm. It explicitly performs a breadth first search of the spatial-tree using peano-code and eliminates additional memory as it uses pre-status significant test for encoding and LSB bits of some coefficients for decoding respectively. This method yields nearly the same performance as SPIHT. This may be desirable in fast and simple hardware implementation and reduces the cost of production because no lists and additional memory are required.