Motivation: Differential coexpression-the alteration of gene coexpression patterns observed in different biological conditions-has been proposed to be a mechanism for revealing rewiring of transcription regulatory networks. Despite wide use of methods for differential coexpression analysis, the phenomenon has not been well-studied. In particular, in many applications, differential coexpression is confounded with differential expression, that is, changes in average levels of expression across conditions. This confounding, despite affecting the interpretation of the differential coexpression, has rarely been studied. Results: We constructed high-quality coexpression networks for five human tissues and identified coexpression links (gene pairs) that were specific to each tissue. Between 3 and 32% of coexpression links were tissue-specific (differentially coexpressed) and this specificity is reproducible in an external dataset. However, we show that up to 75% of the observed differential coexpression is substantially explained by average expression levels of the genes. 'Pure' differential coexpression independent from differential expression is a minority and is less reproducible in external datasets. We also investigated the functional relevance of pure differential coexpression. Our conclusion is that to a large extent, differential coexpression is more parsimoniously explained by changes in average expression levels and pure links have little impact on network-based functional analysis. Supplementary information: Supplementary data are available at Bioinformatics online.