We study a class of ansatz wave functions in which composite fermions form two correlated "partitions." These "bipartite" composite fermion states are demonstrated to be very accurate for electrons in a strong magnetic field interacting via a short-range 3-body interaction potential over a broad range of filling factors. Furthermore, this approach gives accurate approximations for the exact Coulomb ground state at 2+3/5 and 2+4/7 and is thus a promising candidate for the observed fractional quantum Hall states at the hole conjugate fractions at 2+2/5 and 2+3/7.