According to Leo Grammaticus (a collective name for the works related to the Chronicle of Symeon the Logothete, 10th century), Tiberius II was an active builder. Amongst his projects was the construction of the public bath of Blachernai.
Book 2 of the Patria attributes the construction to Leo Makelles (Leo I, r. 401-474), however, it only states that it was "a bath". It cannot be certainly be identified with the public bath.