  In hep-th/0409174, Lin, Lunin and Maldacena constructed a set of regular 1/2
BPS geometries in IIB theory. These remarkable `bubbling AdS' geometries have a
natural interpretation as duals of chiral primary operators with weight Delta=J
in N=4 super-Yang Mills theory. Although these geometries have been assumed to
be complete, from a purely supergravity point of view, additional 1/2 BPS
configurations may potentially exist with a preferred null isometry. We explore
this possibility and prove that the only additional class of 1/2 BPS solutions
with SO(4) x SO(4) isometry are the familiar IIB pp-waves.
