Bicoid is a morphogen that sets up the anterior-posterior axis in early Drosophila embryos. Although the form of the Bicoid profile is consistent with a simple diffusion/degradation model, the observed length scale is much larger than should be expected based on the measured diffusion rate. Here, we study two possible mechanisms that could, in principle, affect this gradient and, hence, address this disagreement. First, we show that including trapping and release of Bicoid by the nuclei during cleavage cycles does not alter the morphogen length scale. More crucially, the inclusion of advective transport due to cytoplasmic streaming can have a large effect. Specifically, we build a simple model based on the (limited) experimental data and show that such a flow can lead to a Bicoid profile that is consistent with various experimental features. Specifically, the observed length scale is obtained, a steady profile is established, and improved scaling between embryos of different lengths is demonstrated.