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Multilingual language models such as mBERT have seen impressive cross-lingual transfer to a variety of languages, but many languages remain excluded from these models. In this paper, we analyse the effect of pre-training with monolingual data for a low-resource language that is not included in mBERT -- Maltese -- with a range of pre-training set ups. We conduct evaluations with the newly pre-trained models on three morphosyntactic tasks -- dependency parsing, part-of-speech tagging, and named-entity recognition -- and one semantic classification task -- sentiment analysis. We also present a newly created corpus for Maltese, and determine the effect that the pre-training data size and domain have on the downstream performance. Our results show that using a mixture of pre-training domains is often superior to using Wikipedia text only. We also find that a fraction of this corpus is enough to make significant leaps in performance over Wikipedia-trained models. We pre-train and compare two models on the new corpus: a monolingual BERT model trained from scratch (BERTu), and a further pre-trained multilingual BERT (mBERTu). The models achieve state-of-the-art performance on these tasks, despite the new corpus being considerably smaller than typically used corpora for high-resourced languages. On average, BERTu outperforms or performs competitively with mBERTu, and the largest gains are observed for higher-level tasks.