  By applying the idea of parafermionic clustering to composite bosons with
positive as well as negative flux, a new series of trial wavefunctions to
describe fractional quantum Hall states is proposed. These non-Abelian states
compete at filling factors k/(3k +/- 2) with other ground states like stripes
or composite fermion states. These two series contain all the states recently
discovered by Pan et al. [Phys. Rev. Lett. 90, 016801 (2003)] including the
even denominator cases. Exact diagonalization studies on the sphere and torus
point to their possible relevance for filling factors 3/7, 3/11, and 3/8.
