The automated detection of cortical lesions (CLs) in patients with multiple sclerosis (MS) is a challenging task that, despite its clinical relevance, has received very little attention. Accurate detection of the small and scarce lesions requires specialized sequences and high or ultra- high field MRI. For supervised training based on multimodal structural MRI at 7T, two experts generated ground truth segmentation masks of 60 patients with 2014 CLs. We implemented a simplified 3D U-Net with three resolution levels (3D U-Net-). By increasing the complexity of the task (adding brain tissue segmentation), while randomly dropping input channels during training, we improved the performance compared to the baseline. Considering a minimum lesion size of 0.75 μL, we achieved a lesion-wise cortical lesion detection rate of 67% and a false positive rate of 42%. However, 393 (24%) of the lesions reported as false positives were post-hoc confirmed as potential or definite lesions by an expert. This indicates the potential of the proposed method to support experts in the tedious process of CL manual segmentation.