Transcription factors (TFs) bind to specific DNA sequences to induce or repress gene expression. Expression levels can be tuned by changing TF concentrations, but the precision of such tuning is limited, since the fraction of time a TF occupies its binding site is subject to stochastic fluctuations. Bicoid (Bcd) is a TF that patterns the early Drosophila embryo by establishing an anterior-to-posterior concentration gradient and activating specific gene targets ("gap genes") in a concentration-dependent manner. Recently, the Bcd gradient and its in-vivo diffusion were quantified in live embryos, raising a quandary: the precision by which the Bcd target genes are defined (one-cell resolution) appeared to exceed the physical limits set by the stochastic binding of Bcd to DNA. We hypothesize that early readout of Bcd could account for the observed precision. Specifically, we consider the possibility that gap genes begin to be expressed earlier than typically measured experimentally, at a time when the distance between the nuclei is large. At this time, the difference in Bcd concentration between adjacent nuclei is large, enabling better tolerance for measurement imprecision. We show that such early decoding can indeed increase the accuracy of gap-gene expression, and that the initial pattern can be stabilized during subsequent divisions.