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This paper studies the fine-grain scalable compression problem with emphasis on 1-D signals such as audio signals. Like in the successful 2-D still image compression techniques embedded zerotree wavelet coder (EZW) and set partitioning in hierarchical trees (SPIHT), the desired fine-granular scalability and high coding efficiency are benefited from a tree-based significance mapping technique. A significance tree serves to quickly locate and efficiently encode the important coefficients in the transform domain. The aim of this paper is to find such suitable significance trees for compressing dynamically variant 1-D signals. The proposed solution is a novel dynamic significance tree (DST) where, unlike in existing solutions with a single type of tree, a significance tree is chosen dynamically out of a set of trees by taking into account the actual coefficients distribution. We show how a set of possible DSTs can be derived that is optimized for a given (training) dataset. The method outperforms the existing scheme for lossy audio compression based on a single-type tree (SPIHT) and the scalable audio coding schemes MPEG-4 BSAC and MPEG-4 SLS. For bitrates less than 32 kbps, it results in an improved perceived audio quality compared to the fixed-bitrate MPEG-2/4 AAC audio coding scheme while providing progressive transmission and finer scalability.