  Cha and Kim proved that if a knot K is not algebraically slice, then no
iterated Bing double of K is concordant to the unlink. We prove that if K has
nontrivial signature $\sigma$, then the n-iterated Bing double of K is not
concordant to any boundary link with boundary surfaces of genus less than
$2^{n-1}\sigma$. The same result holds with $\sigma$ replaced by $2\tau$, twice
the Ozsvath-Szabo knot concordance invariant.
