I have a rather small CBB with a medium/large sized Mi. I also have 2 medium Yellow Tangs .There seems to be no problem with the Tangs and the Copperband(the CBB was introduced mid December).The Moorish Idol(it is more than double the size of the CBB)does chase the CBB once in a while,but does not create problem.The CBB swims freely about.It also gets chased by my Singapoor Angel,however,there isn't any real aggressiveness,displayed by any inhabitants.
There was a comment recently that maybe if you have a small CBB the other fish won't feel threatened by it,and it will not get attacked.That seems to fit my case.The most challenging interactions is coming from the Singapoor Angel.It is the same size as the CBB.I don't know what to advise you .A lot has to do with the size of your aquarium and hiding places,too.