  We compute lattice renormalisation constants of local bilinear quark
operators for overlap fermions and improved gauge actions. Among the actions we
consider are the Symanzik, L\"uscher-Weisz, Iwasaki and DBW2 gauge actions. The
results are given for a variety of $\rho$ parameters. We show how to apply mean
field (tadpole) improvement to overlap fermions. The question, what is a good
gauge action, is discussed from the perturbative point of view. Finally, we
show analytically that the gauge dependent part of the self-energy and the
amputated Green functions are independent of the lattice fermion
representation, using either Wilson or overlap fermions.
