This paper describes our submission to the DISRPT2021 Shared Task on Discourse Unit Segmentation, Connective Detection, and Relation Classification. Our system, called DisCoDisCo, is a Transformer-based neural classifier which enhances contextualized word embeddings (CWEs) with hand-crafted features, relying on tokenwise sequence tagging for discourse segmentation and connective detection, and a feature-rich, encoder-less sentence pair classifier for relation classification. Our results for the first two tasks outperform SOTA scores from the previous 2019 shared task, and results on relation classification suggest strong performance on the new 2021 benchmark. Ablation tests show that including features beyond CWEs are helpful for both tasks, and a partial evaluation of multiple pre-trained Transformer-based language models indicates that models pre-trained on the Next Sentence Prediction (NSP) task are optimal for relation classification.