  We report on non-perturbative computations of the improvement coefficient c_V
and the renormalization factor Z_V of the vector current in three-flavour O(a)
improved lattice QCD with Wilson quarks and tree-level Symanzik improved gauge
action. To reduce finite quark mass effects, our improvement and normalization
conditions exploit massive chiral Ward identities formulated in the
Schroedinger functional setup, which also allow deriving a new method to
extract the ratio Z_S/Z_P of scalar to pseudoscalar renormalization constants.
We present preliminary results of a numerical evaluation of Z_V and c_V along a
line of constant physics with gauge couplings corresponding to lattice spacings
of about 0.09 fm and below, relevant for phenomenological applications.
