Segmentation is the first step in building practical discourse parsers, and is often neglected in discourse parsing studies. The goal is to identify the minimal spans of text to be linked by discourse relations, or to isolate explicit marking of discourse relations. Existing systems on English report F1 scores as high as 95%, but they generally assume gold sentence boundaries and are restricted to En-glish newswire texts annotated within the RST framework. This article presents a generic approach and a system, ToNy, a discourse segmenter developed for the DisRPT shared task where multiple discourse representation schemes, languages and domains are represented. In our experiments, we found that a straightforward sequence prediction architecture with pretrained contextual embeddings is sufficient to reach performance levels comparable to existing systems, when separately trained on each corpus. We report performance between 81% and 96% in F1 score. We also observed that discourse segmentation models only display a moderate generalization capability, even within the same language and discourse representation scheme.