  We show that if K is any knot whose Ozsvath-Szabo concordance invariant
tau(K) is positive, the all-positive Whitehead double of any iterated Bing
double of K is topologically but not smoothly slice. We also show that the
all-positive Whitehead double of any iterated Bing double of the Hopf link
(e.g., the all-positive Whitehead double of the Borromean rings) is not
smoothly slice; it is not known whether these links are topologically slice.
