Transition from ν=8/5 to ν=5/3 in the low Zeeman energy limit

Skyrmions in the FQHE at filling fractions above \nu=1/3 are studied within the anyon model and by exact diagonalization. Relations to the composite fermion theory are pointed out. We find that unpolarized quasiparticles above \nu=1/3 are stable below B\approx 0.02T. At low Zeeman energy the polarization in the range \nu=8/5 ... 5/3 is found to be a linear function of the filling factor. We also reexamine the energy and wave function of skyrmions at \nu=1 by a new method.