We construct a family of local static, vacuum five-dimensional solutions with
two commuting spatial isometries describing a black hole with a $S^3$ horizon
and a 2-cycle `bubble' in the domain of outer communications. The solutions are
obtained by adding distortions to an asymptotically flat seed solution. We show
that the conical singularities in the undistorted geometry can be removed by an
appropriate choice of the distortion.