  We discuss the improvement of flavour non-singlet point and one-link lattice
quark operators, which describe the quark currents and the first moment of the
DIS structure functions respectively. Suitable bases of improved operators are
given, and the corresponding renormalisation factors and improvement
coefficients are calculated in one-loop lattice perturbation theory, using the
Sheikholeslami-Wohlert (clover) action. To this order we achieve off-shell
improvement by eliminating the effect of contact terms. We use massive
fermions, and our calculations are done keeping all terms up to first order in
the lattice spacing, for arbitrary m^2/p^2, in a general covariant gauge. We
also compare clover fermions with fermions satisfying the Ginsparg-Wilson
relation, and show how to remove O(a) effects off-shell in this case too, and
how this is in many aspects simpler than for clover fermions. Finally, tadpole
improvement is also considered.
