In this paper, an enhanced version of Embedded zerotree wavelet (EZW) image coding algorithm is proposed, referred to as EZW-SC. By exploiting a new principle that relies on a subband classification concept, the enhanced algorithm allows the prediction of insignificant subbands at early passes, along with the use of an improved significance map. This reduces the redundancy of zerotree symbols, speeds up the coding process and improves the coding of significant coefficients. In fact, the EZW-SC algorithm scans only significant subbands and significantly improves the lossy compression performance with the conventional EZW. Moreover, new EZW-based schemes are presented to perform colour image coding by taking advantage of the interdependency of the colour components. Experimental results show clear superiority of the proposed algorithms over the conventional EZW as well as other related EZW schemes at various bit rates in both greyscale and colour image compression.