This paper describes a technique for estimating the Kullback-Leibler (KL) distance between two Hidden Markov Models (HMMs), and for measuring the quality of the estimator. It also provides some results based on applying the technique to wavelet domain Hidden Markov Tree (HMT) models used in image segmentation. The technique is easily applied, because in most situations the necessary tools (data generation and likelihood calculation) are already in place.