Apparatus and method for encoding zerotrees in a wavelet-based coding technique. The method uses a depth-first pattern for traversing the zerotree, i.e., each branch of the tree, from parent to child to grandchild and so on, is fully traversed before a next branch is traversed. The depth-first tree traversal pattern is used to quantize the coefficients of the tree as well as to assign symbols to the quantized coefficients. The method assigns one of three symbols to each node: ZEROTREE ROOT, VALUED ZEROTREE ROOT, and VALUE. By using three symbols and the efficient tree traversal pattern, the method is substantially more efficient at encoding a zerotree than the prior art. Additionally, this concept is applied to the encoding of “vector” zerotrees.