Deep learning-based language models pretrained on large unannotated text corpora have been demonstrated to allow efficient transfer learning for natural language processing, with recent approaches such as the transformer-based BERT model advancing the state of the art across a variety of tasks. While most work on these models has focused on high-resource languages, in particular English, a number of recent efforts have introduced multilingual models that can be fine-tuned to address tasks in a large number of different languages. However, we still lack a thorough understanding of the capabilities of these models, in particular for lower-resourced languages. In this paper, we focus on Finnish and thoroughly evaluate the multilingual BERT model on a range of tasks, comparing it with a new Finnish BERT model trained from scratch. The new language-specific model is shown to systematically and clearly outperform the multilingual. While the multilingual model largely fails to reach the performance of previously proposed methods, the custom Finnish BERT model establishes new state-of-the-art results on all corpora for all reference tasks: part-of-speech tagging, named entity recognition, and dependency parsing. We release the model and all related resources created for this study with open licenses at this https URL .