The information bottleneck method is an unsupervised model independent data organization technique. Given a joint distribution P(A,B), this method constructs a new variable T that extracts partitions, or clusters, over the values of ,4 that are informative about B. In a recent paper, we introduced a general principled framework for multivariate extensions of the information bottleneck method that allows us to consider multiple systems of data partitions that are inter-related. In this paper, we present a new family of simple agglomerative algorithms to construct such systems of inter-related clusters. We analyze the behavior of these algorithms and apply them to several real-life datasets.