  In a recent work we showed that for a Hamiltonian system with constraints,
the set of constraints can be investigated in first and second class constraint
chains. We show here that using this "chain by chain" method for an arbitrary
system one can fix the gauges in the most economical and consistent way. We
show that it is enough to assume some gauge fixing conditions conjugate to last
elements of first class chains. The remaining necessary conditions would emerge
from consistency conditions.
