A technique for directly designing a variable-rate tree-structured vector quantizer by growing the tree one node at a time rather than one layer at time is presented. The technique is a natural extension of a tree growing method for decision trees. When the tree is pruned with a generalized algorithm for optimally pruning trees, improvement is measured in the signal-to-noise ratio at high rates over pruning a fixed-rate tree-structured vector quantizer of the same initial rate. The growing algorithm can be interpreted as a constrained inverse of the pruning algorithm. >