Microarray data provides a pcrfcct riposte to the original assumption underlying association rule mining - large but sparse transaction sets. Tn a typical microarray the number of columns (genes) is an order of magnitude larger than the number of rows (experiments). A new family of row enumerated rule mining algorithms have emerged to facilitate mining in dense sets. However, to date, all the algorithms proposed to mine expression relationships alone rely on the support measure to prune the search space. This is a major shortcoming as it results in the pruning of many potentially interesting rules which have low support but high confidence. In this paper we propose the MaxConf algorithm which exploits the weak downward closure of confidence to directly mine for high confidence rules. We also provide a means to evaluate the biological significance of the gene relationships identified. An evaluation of MaxConf with RERTT on the database BIND shows that their recall is 94% and .15% respectively.