In this discussion, we would like to contribute our thoughts on how to construct the matched pairs. Greevy, Lu, Silber and Rosenbaum (2004) point out that in most randomized studies, only one or two variables are used in constructing the pairs. To remedy this, Greevy et al. present a method for optimal multivariate matching. They demonstrate in an example with 14 covariates and 132 units that the optimal matching achieves substantially better balance on all 14 covariates than an unmatched design. Greevy et al. considered the situation in which we want to use all available units in the experiment. In cluster randomized studies, because of cost considerations, we can often only use some of the clusters, that is, there are N = 2k clusters but we would only like to include 2m (m