The currently practiced methods of significance testing in microarray gene expression profiling are highly unstable and tend to be very low in power. These undesirable properties are due to the nature of multiple testing procedures, as well as extremely strong and long-ranged correlations between gene expression levels. In an earlier publication, we identified a special structure in gene expression data that produces a sequence of weakly dependent random variables. This structure, termed the delta-sequence, lies at the heart of a new methodology for selecting differentially expressed genes in nonoverlapping gene pairs. The proposed method has two distinct advantages: (1) it leads to dramatic gains in terms of the mean numbers of true and false discoveries, and in the stability of the results of testing; and (2) its outcomes are entirely free from the log-additive array-specific technical noise. We demonstrate the usefulness of this approach in conjunction with the nonparametric empirical Bayes method. The proposed modification of the empirical Bayes method leads to significant improvements in its performance. The new paradigm arising from the existence of the delta-sequence in biological data offers considerable scope for future developments in this area of methodological research.