This is joint work with Emily Cliff and Charles Paquette. Given a quiver, a dimension vector and a stability condition, Alistair King shows that, if the dimension vector is unimodular, there is a moduli space of stable representations with a universal representation. We extend this result to show that even when the dimension vector is divisible, the moduli space constructed by King has a quasi-universal representation. We are able to use the quasi-universal representation to construct generic bricks in several cases.