The Helsinki-NLP team participated in the NADI 2023 shared tasks on Arabic dialect translation with seven submissions. We used statistical (SMT) and neural machine translation (NMT) methods and explored characterand subword-based data preprocessing. Our submissions placed second in both tracks. In the open track, our winning submission is a character-level SMT system with additional Modern Standard Arabic language models. In the closed track, our best BLEU scores were obtained with the leave-as-is baseline, a simple copy of the input, and narrowly followed by SMT systems. In both tracks, fine-tuning existing multilingual models such as AraT5 or ByT5 did not yield superior performance compared to SMT.