Galaxies acting as gravitational lenses are surrounded by, at most, a handful of images. This apparent paucity of information forces one to make the best possible use of what information is available to invert the lens system. In this paper, we explore the use of a genetic algorithm to invert in a non-parametric way strong lensing systems containing only a small number of images. Perhaps the most important conclusion of this paper is that it is possible to infer the mass distribution of such gravitational lens systems using a non-parametric technique. We show that including information about the null space (i.e. the region where no images are found) is prerequisite to avoid the prediction of a large number of spurious images, and to reliably reconstruct the lens mass density. While the total mass of the lens is usually constrained within a few percent, the fidelity of the reconstruction of the lens mass distribution depends on the number and position of the images. The technique employed to include null space information can be extended in a straightforward way to add additional constraints, such as weak lensing data or time delay information.
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