The street was originally a canal but was then filled in (rio terà), and appears to have been named after a certain Barba who was a greengrocer (frutarol). According to other theories, it derives from the old name of Baduario (after a certain Badoaro), which was shortened to Barba. 

Local anecdotes tell of the first bridge here which was torn down so that a more conveniently-located one could be built for Prince Cicogna for his walk to mass at the Chiesa dei Crociferi in today’s Campo dei Gesuiti. Note the inset Gothic shield (a chiselled banded weapon) with a serrated horizontal edge and the angel’s hips merging with the shield’s lines.