The early Drosophila embryo is patterned by graded distributions of maternal transcription factors. Recent studies revealed that pattern formation by these graded signals depends on uniformly expressed transcriptional activators, such as Zelda. Removal of Zelda influences both the timing and the spatial expression domains for most of the genes controlled by maternal gradients. We demonstrate that some of these patterning defects, which range from temporal delay to loss of expression, can be rationalized with the use of a mathematical model based on cooperative binding of graded and uniform factors. This model makes a number of predictions, which we confirm experimentally by analyzing the expression of short gastrulation (sog), a gene that is controlled by a combination of the Dorsal morphogen gradient and Zelda. The proposed model suggests a general mechanism for the formation of nested gene expression domains, which is a hallmark of tissue patterning by morphogen gradients. According to this mechanism, the differential effects of a morphogen on its target genes can depend on their differential sensitivity to uniform factors.