This paper presents DeepSPIN’s submissions to the SIGMORPHON 2022 Shared Task on Morpheme Segmentation. We make three submissions, all to the word-level subtask. First, we show that entmax-based sparse sequence-tosequence models deliver large improvements over conventional softmax-based models, echoing results from other tasks. Then, we challenge the assumption that models for morphological tasks should be trained at the character level by building a transformer that generates morphemes as sequences of unigram language model-induced subwords. This subword transformer outperforms all of our character-level models and wins the word-level subtask. Although we do not submit an official submission to the sentence-level subtask, we show that this subword-based approach is highly effective there as well.