The analysis of the quantum Hall response of a small system of interacting ultracold bosonic atoms through the variation of its Hall resistivity against the applied gauge magnetic field provides a powerful method to unmask its strongly correlated states in a quite exhaustive way. Within a fixed range of vaues of the magnetic field in the lowest Landau-level regime, where the resistivity displays two succesive plateaux, we identify the implied states as the Pfaffian and the state with filling factor \nu=2/3 in the thermodinamic limit. We fix the conditions to have good observability.