  We investigate the construction of five-dimensional, three-charge
supergravity solutions that only have a rotational U(1) isometry. We show that
such solutions can be obtained as warped compactifications with a singular
ambi-polar hyper-Kahler base space and singular warp factors. We show that the
complete solution is regular around the critical surface of the ambi-polar
base. We illustrate this by presenting the explicit form of the most general
supersymmetric solutions that can be obtained from an Atiyah-Hitchin base space
and its ambi-polar generalizations. We make a parallel analysis using an
ambi-polar generalization of the Eguchi-Hanson base space metric. We also show
how the bubbling procedure applied to the ambi-polar Eguchi-Hanson metric can
convert it to a global AdS_2xS^3 compactification.
