Many commentators suppose that Anaximander subscribes to a multiple worlds thesis. In particular, they assume that: either Anaximander accepts that there are innumerable co-existent worlds, or he accepts that there are innumerable successive worlds. The first of these interpretations has been shown to be problematic. In this discussion note I present two new arguments against the multiple successive worlds reading of Anaximander, with the intent to buttress a single world reconstruction of his cosmology.