  We construct new asymptotically AdS_4 solutions dual to 2+1 CFTs at finite
density and zero temperature by combining the ingredients of the electron star
and the holographic superconductor. The solutions, which we call "compact
electron stars", contain both a fermionic fluid and charged scalar hair in the
bulk. We show that the new solutions are thermodynamically favoured in the
region of parameter space where they exist. Along the boundary of this region,
we find evidence for a continuous phase transition between the holographic
superconductor and the compact star solution.
