Computational models of enhancer function generally assume that transcription factors (TFs) exert their regulatory effects independently, modeling an enhancer as a "bag of sites." These models fail on endogenous loci that harbor multiple enhancers, and a "two-tier" model appears better suited: in each enhancer TFs work independently, and the total expression is a weighted sum of their expression readouts. Here, we test these two opposing views on how cis-regulatory information is integrated. We fused two Drosophila blastoderm enhancers, measured their readouts, and applied the above two models to these data. The two-tier mechanism better fits these readouts, suggesting that these fused enhancers comprise multiple independent modules, despite having sequence characteristics typical of single enhancers. We show that short-range TF-TF interactions are not sufficient to designate such modules, suggesting unknown underlying mechanisms. Our results underscore that mechanisms of how modules are defined and how their outputs are combined remain to be elucidated.