Tweakable blockcipher (TBC) is a powerful tool to design authenticated encryption schemes as illustrated by Minematsu's Offset Two Rounds (OTR) construction. It considers an additional input, called tweak, to a standard blockcipher which adds some variability to this primitive. More specifically, each tweak is expected to define a different, independent pseudo-random permutation. In this work we focus on OTR's way to instantiate a TBC and show that it does not achieve independence for a large amount of parameters. We indeed describe collisions between the input masks derived from the tweaks and explain how they result in practical attacks against this scheme, breaking privacy, authenticity, or both, using a single encryption query, with advantage at least 1/4. We stress however that our results do not invalidate the OTR construction as a whole but simply prove that the TBC's input masks should be designed differently.