This paper describes the University of Helsinki's submissions to the WMT18 shared news translation task for English-Finnish and English-Estonian, in both directions. This year, our main submissions employ a novel neural architecture, the Transformer, using the open-source OpenNMT framework. Our experiments couple domain labeling and fine tuned multilingual models with shared vocabularies between the source and target language, using the provided parallel data of the shared task and additional back-translations. Finally, we compare, for the English-to-Finnish case, the effectiveness of different machine translation architectures, starting from a rule-based approach to our best neural model, analyzing the output and highlighting future research.