Many genes determining cell identity are regulated by clusters of Mediator-bound enhancer elements collectively referred to as super-enhancers. These super-enhancers have been proposed to manifest higher-order properties important in development and disease. Here we report a comprehensive functional dissection of one of the strongest putative super-enhancers in erythroid cells. By generating a series of mouse models, deleting each of the five regulatory elements of the α-globin super-enhancer individually and in informative combinations, we demonstrate that each constituent enhancer seems to act independently and in an additive fashion with respect to hematological phenotype, gene expression, chromatin structure and chromosome conformation, without clear evidence of synergistic or higher-order effects. Our study highlights the importance of functional genetic analyses for the identification of new concepts in transcriptional regulation.