  The gauge-invariance properties and singularity elimination of the modified
perturbation theory for QCD introduced in previous works, are investigated. The
construction of the modified free propagators is generalized to include the
dependence on the gauge parameter $\alpha $. Further, a functional proof of the
independence of the theory under the changes of the quantum and classical
gauges is given. The singularities appearing in the perturbative expansion are
eliminated by properly combining dimensional regularization with the Nakanishi
infrared regularization for the invariant functions in the operator
quantization of the $\alpha$-dependent gauge theory. First-order evaluations of
various quantities are presented, illustrating the gauge invariance-properties.
