  We present two new suggestions for density of states (DoS) approaches to
finite density lattice QCD. Both proposals are based on the recently developed
and successfully tested DoS FFA technique, which is a DoS approach for bosonic
systems with a complex action problem. The two different implementations of DoS
FFA we suggest for QCD make use of different representations of finite density
lattice QCD in terms of suitable pseudo-fermion path integrals. The first
proposal is based on a pseudo-fermion representation of the grand canonical QCD
partition sum, while the second is a formulation for the canonical ensemble. We
work out the details of the two proposals and discuss the results of
exploratory 2-d test studies for free fermions at finite density, where exact
reference data allow one to verify the final results and intermediate steps.
