  We investigate giant and dual giant type BPS configurations in the
near-horizon geometry of a certain 1/16-BPS AdS_5 black hole. By quantising the
space of solutions we count the dual giant configurations and compare with the
black hole entropy. This suggests a missing degeneracy factor which we argue
comes from an angular momentum quantum number. From the D-brane world volume
this arises from BPS electromagnetic waves. We study these waves in the context
of giants and dual giants in the black hole near-horizon geometry. We further
demonstrate that turning on waves on the world-volume of 1/8-BPS dual giants in
AdS_5 x S^5 leads to 1/16-BPS states with an additional angular momentum
quantum number.
