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Deep learning has led to great progress in the detection of mobile (i.e. movement-capable) objects in urban driving scenes in recent years. Supervised approaches typically require the annotation of large training sets; there has thus been great interest in leveraging weakly, semi- or self-supervised methods to avoid this, with much success. Whilst weakly and semi-supervised methods require some annotation, self-supervised methods have used cues such as motion to relieve the need for annotation altogether. However, a complete absence of annotation typically degrades their performance, and ambiguities that arise during motion grouping can inhibit their ability to find accurate object boundaries. In this paper, we propose a new self-supervised mobile object detection approach called SCT. This uses both motion cues and expected object sizes to improve detection performance, and predicts a dense grid of 3D oriented bounding boxes to improve object discovery. We significantly outperform the state-of-the-art self-supervised mobile object detection method TCR on the KITTI tracking benchmark, and achieve performance that is within 30% of the fully supervised PV-RCNN++ method for IoUs <= 0.5.