  We present a pair of joint conditions on the two functions $b_1,b_2$ strictly
weaker than $b_1,b_2\in \operatorname{BMO}$ that almost characterize the $L^2$
boundedness of the iterated commutator $[b_2,[b_1,T]]$ of these functions and a
Calder\'on-Zygmund operator $T.$ Namely, we sandwich this boundedness between
two bisublinear mean oscillation conditions of which one is a slightly bumped
up version of the other.
