  We construct BPS geometries describing normalizable excitations of AdS_2 x
S^2. All regular horizon-free solutions are parameterized by two harmonic
functions in R^3 with sources along closed curves. This local structure is
reminiscent of the "bubbling solutions" for the other AdS cases, however, due
to peculiar asymptotic properties of AdS_2, one copy of R^3 does not cover the
entire space, and we discuss the procedure for analytic continuation, which
leads to a nontrivial topological structure of the new geometries. We also
study supersymmetric brane probes on the new geometries, which represent the
AdS_2 x S^2 counterparts of the giant gravitons.
