Crusadecat,
Another Mickey Cohen also fought at about the same time--<a href="http://www.boxrec.com/boxer_display.php?boxer_id=047585" target="_blank">"Irish" Mickey Cohen</a>, a lightweight out of Denver, who boxed from 1926 to 1935. He faced some good fighters: Baby Arizmendi, Chalky Wright, Varias Milling, Harry Dublinsky, all of whom he lost to. He did beat Mike Dundee, Dublinsky once, Tommy Grogan, Davey Abad, and Memphis Pal Moore.
Perhaps he should be rated 3, with "Gangster" Mickey Cohen a 1.