The state-of-the-art method for automatically segmenting white matter bundles in diffusion-weighted MRI is tractography in conjunction with streamline cluster selection. This process involves long chains of processing steps which are not only computationally expensive but also complex to setup and tedious with respect to quality control. Direct bundle segmentation methods treat the task as a traditional image segmentation problem. While they so far did not deliver competitive results, they can potentially mitigate many of the mentioned issues. We present a novel supervised approach for direct tract segmentation that shows major performance gains. It builds upon a stacked U-Net architecture which is trained on manual bundle segmentations from Human Connectome Project subjects. We evaluate our approach \textit{in vivo} as well as \textit{in silico} using the ISMRM 2015 Tractography Challenge phantom dataset. We achieve human segmentation performance and a major performance gain over previous pipelines. We show how the learned spatial priors efficiently guide the segmentation even at lower image qualities with little quality loss.