A method, system and computer program product are provided for progressively encoding a digitized color image using a data processing system, the digitized color image being provided by assigning each of the M distinct colors to at least one pixel in the set of pixels. This involves initializing and growing the tree structure by selecting a leaf node n to become a non-leaf node n linked to two new leaf nodes based on an associated achievable cost, wherein the associated achievable cost is based on 1) a determined associated change in distortion resulting from turning the leaf node into the non-leaf node linked to the two new leaf nodes; and 2) a determined associated increase in entropy rate resulting from turning the leaf node into the non-leaf node linked to the two new leaf nodes.