  We split the Yang-Mills Lagrangian into a free and an interaction part in
such a way, that the free part is non-local and contains an arbitrary form
factor.
  Manifest gauge invariance is guaranteed by connecting the field-strength
tensors at different space-time points by a string. As a result the gluon
propagator, which, due to the presence of the string, now contains many
different contributions, comes out strictly transversal in one-loop order.
  We also calculate the ghost self-energy and the ghost-gluon vertex in
one-loop order. Subsequently we discuss how one can determine the "optimal"
form of the form factor. To apply well known principles like "fastest apparent
convergence" or "principle of minimal sensitivity" one has first to solve some
problems connected with divergences and renormalization. Here we concentrate on
the calculation of the anomalous dimensions and the beta-function. This is
technically simpler because only the divergent contributions of the integrals
have to be determined. The beta-function becomes independent of the gauge
parameter as it should. A puzzle with respect to the principle of minimal
sensitivity shows up. Really interesting non-perturbative results are expected
when applying the above principles directly to the propagator. For the
beta-function a two loop calculation would be required to obtain non-trivial
results.
