Are there compact heavy four-quark bound states?

We present an exact method to study four-quark systems based on the hyperspherical harmonics formalism. We apply it to several physical systems of interest containing two heavy and two light quarks using different quark-quark potentials. Our conclusions mark the boundaries for the possible existence of compact, nonmolecular, four-quark bound states. While QQn̄n̄ states may be stable in nature, the stability of QQ̄nn̄ states would imply the existence of quark correlations not taken into account by simple quark dynamical models.