  We consider the problem of covariant gauge-fixing in the most general setting
of the field-antifield formalism, where the action W and the gauge-fixing part
X enter symmetrically and both satisfy the Quantum Master Equation. Analogous
to the gauge-generating algebra of the action W, we analyze the possibility of
having a reducible gauge-fixing algebra of X. We treat a reducible gauge-fixing
algebra of the so-called first-stage in full detail and generalize to arbitrary
stages. The associated "square root" measure contributions are worked out from
first principles, with or without the presence of antisymplectic second-class
constraints. Finally, we consider an W-X alternating multi-level
generalization.
