State-of-the-art machine translation (MT) systems rely on the availability of large parallel corpora, containing millions of sentence pairs. For the Icelandic language, the parallel corpus ParIce exists, consisting of about 3.6 million English-Icelandic sentence pairs. Given that parallel corpora for low-resource languages typically contain sentence pairs in the tens or hundreds of thousands, we classify Icelandic as a medium-resource language for MT purposes. In this paper, we present on-going experiments with different MT models, both statistical and neural, for translating English to Icelandic based on ParIce. We describe the corpus and the filtering process used for removing noisy segments, the different models used for training, and the preliminary automatic and human evaluation. We find that, while using an aggressive filtering approach, the most recent neural MT system (Transformer) performs best, obtaining the highest BLEU score and the highest fluency and adequacy scores from human evaluation for in-domain translation. Our work could be beneficial to other languages for which a similar amount of parallel data is available.