We present the system submission from the FASTPARSE team for the EUD Shared Task at IWPT 2021. We engaged in the task last year by focusing on efficiency. This year we have focused on experimenting with new ideas on a limited time budget. Our system is based on splitting the EUD graph into several trees, based on linguistic criteria. We predict these trees using a sequence-labelling parser and combine them into an EUD graph. The results were relatively poor, although not a total disaster and could probably be improved with some polishing of the system's rough edges.