  Nonsingularity conditions are established for the BFV gauge-fixing fermion
which are sufficient for it to lead to the correct path integral for a theory
with constraints canonically quantized in the BFV approach. The conditions
ensure that anticommutator of this fermion with the BRST charge regularises the
path integral by regularising the trace over non-physical states in each ghost
sector. The results are applied to the quantization of a system which has a
Gribov problem, using a non-standard form of the gauge-fixing fermion.
