It is sometimes impossible to construct a relativistic star cluster with the same structure as a given relativistic fluid sphere. The reason is the unphysical nature of the distribution function which is sometimes negative in part of phase-space or sometimes contains non-integrable singularities. A simple test is derived that can be applied to a given fluid sphere to provide a set of sufficient conditions for the distribution function to be unphysical. The test is applied to some fluid spheres and clusters that have been studied in the literature.