  The coefficient c_A required for O(a) improvement of the axial current in
lattice QCD with N_f=3 flavors of Wilson fermions and the tree-level
Symanzik-improved gauge action is determined non-perturbatively. The standard
improvement condition using Schroedinger functional boundary conditions is
employed at constant physics for a range of couplings relevant for simulations
at lattice spacings of ~ 0.09 fm and below. We define the improvement condition
projected onto the zero topological charge sector of the theory, in order to
avoid the problem of possibly insufficient tunneling between topological
sectors in our simulations at the smallest bare coupling. An interpolation
formula for c_A(g_0^2) is provided together with our final results.
