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Inspired by recent research, we explore ways to model the highly morphological Finnish language at the level of characters while maintaining the performance of word-level models. We propose a new Character-to-Word-to-Character (C2W2C) compositional language model that uses characters as input and output while still internally processing word level embeddings. Our preliminary experiments, using the Finnish Europarl V7 corpus, indicate that C2W2C can respond well to the challenges of morphologically rich languages such as high out of vocabulary rates, the prediction of novel words, and growing vocabulary size. Notably, the model is able to correctly score inflectional forms that are not present in the training data and sample grammatically and semantically correct Finnish sentences character by character.