A gauge-averaging functional of the axial type is studied for simple supergravity at one loop about hat Euclidean four-space bounded by a three-sphere, or two concentric three-spheres. This is a generalization of recent work on the axial gauge in quantum supergravity on manifolds with boundary. Ghost modes obey nonlocal boundary conditions of the spectral type, in that half of them obey Dirichlet or Neumann conditions at the boundary. In both cases, they give a vanishing contribution to the one-loop divergence. The admissibility of noncovariant gauges at the classical level is also proved.
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