We present the Uppsala system for the CoNLL 2018 Shared Task on universal dependency parsing. Our system is a pipeline consisting of three components: the first performs joint word and sentence segmentation; the second predicts part-ofspeech tags and morphological features; the third predicts dependency trees from words and tags. Instead of training a single parsing model for each treebank, we trained models with multiple treebanks for one language or closely related languages, greatly reducing the number of models. On the official test run, we ranked 7th of 27 teams for the LAS and MLAS metrics. Our system obtained the best scores overall for word segmentation, universal POS tagging, and morphological features.