  We propose a novel infinite-volume brane world scenario where we live on a
non-inflating spherical 3-brane, whose radius is somewhat larger than the
present Hubble size, embedded in higher dimensional bulk. Once we include
higher curvature terms in the bulk, we find completely smooth solutions with
the property that the 3-brane world-volume is non-inflating for a continuous
range of positive values of the brane tension, that is, without fine-tuning. In
particular, our solution, which is a near-BPS background with supersymmetry
broken on the brane around TeV, is controlled by a single integration constant.
