In this paper, we report on an unsupervised greedy-style process for acquiring phrase translations from sentence-aligned parallel corpora. Thanks to innovative selection strategies, this process can acquire multiple translations without size criteria, i.e. phrases can have several translations, can be of any size, and their size is not considered when selecting their translations. Even though the process is in an early development stage and has much room for improvements, evaluation shows that it yields phrase translations of high precision that are relevant to machine translation but also to a wider set of applications including memory-based translation or multi-word acquisition.