  We consider a gauge-invariant, mass-independent prescription for
renormalizing composite operators, regularized on the lattice, in the spirit of
the coordinate space (X-space) renormalization scheme. The prescription
involves only Green's functions of products of gauge-invariant operators,
situated at distinct space-time points, in a way as to avoid potential contact
singularities. Such Green's functions can be computed nonperturbatively in
numerical simulations, with no need to fix a gauge: thus, renormalization to
this "intermediate" scheme can be carried out in a completely nonperturbative
manner.
  Expressing renormalized operators in the $\overline{\rm MS}$ scheme requires
the calculation of corresponding conversion factors. The latter can only be
computed in perturbation theory, by the very nature of the $\overline{\rm MS}$;
however, the computations are greatly simplified by virtue of the following
attributes: i) In the absense of operator mixing, they involve only massless,
two-point functions; such quantities are calculable to very high perturbative
order. ii) They are gauge invariant; thus, they may be computed in a convenient
gauge. iii) Where operator mixing may occur, only gauge-invariant operators
will appear in the mixing pattern: Unlike other schemes, involving mixing with
gauge-variant operators (which may contain ghost fields), the mixing matrices
in the present scheme are greatly reduced. Still, computation of some
three-point functions may not be altogether avoidable.
  We exemplify the procedure by computing, to lowest order, the conversion
factors for fermion bilinear operators of the form $\bar\psi\Gamma\psi$ in QCD.
We also employ the gauge-invariant scheme in the study of mixing between gluon
and quark energy-momentum tensor operators: We compute to one loop the
conversion factors relating the nonperturbative mixing matrix to the
$\overline{\rm MS}$ scheme.
