A general introduction to the topological mechanism responsible for the absolute confinement of quarks inside hadronic bound states is given, including the effects of a finite instanton angle. We then propose a calculational technique for computing these states and their properties, where instead of topology we rely on a perturbative mechanism. It assumes that already before the topological mechanism can come into effect there is already a strong inclination of quarks to be confined. In particular the planar limit of large N QCD should exhibit this mechanism. By renormalizing the infrared divergence of one-loop diagrams, one may already realize a confining potential. In practice, our procedure will require gauge-fixing in advance, but it would be more elegant if, at an intermediate level, the theory with infrared counter terms included could be written as a gauge-invariant effective model. Models of the desired kind are described. They are not renormalizable, but they are local, gauge- and lorentz invariant.