In the context of brane cosmology, a scenario where our universe is a 3+1-dimensional surface (the “brane”) embedded in a five-dimensional spacetime (the “bulk”), we focus on geometries for which the brane is anisotropic though still homogeneous. The main question we address is the following: can an anisotropic brane be sourced by a perfect fluid? As opposed to standard 4D cosmology, we argue that this may only be possible for very specific perfect fluid sources.