  We report on a non-perturbative computation of the renormalization factor Z_A
of the axial vector current in three-flavour O(a) improved lattice QCD with
Wilson quarks and tree-level Symanzik improved gauge action and also recall our
recent determination of the improvement coefficient c_A. Our normalization and
improvement conditions are formulated at constant physics in a Schr\"odinger
functional setup. The normalization condition exploits the full, massive axial
Ward identity to reduce finite quark mass effects in the evaluation of Z_A and
correlators with boundary wave functions to suppress excited state
contributions in the pseudoscalar channel.
