Invasive pests threaten food security and devastate ecosystems. A universal problem in the management of such species is that small populations can easily evade detection. This makes identifying new incursions challenging and also complicates efforts to eradicate or contain established populations. If invasive populations exhibited strong Allee effects, such that small populations tend towards extinction, then many of the issues associated with detecting small populations could be avoided; these populations would go extinct without intervention. Of course, invasive species rarely exhibit a strong Allee effect, but new genetic technologies mean that it is conceivable to impose one. Here we consider whether genetic Allee effects could be used to control invasive species. We examine the simple situation of founder establishment to test this idea. We use numerical and individual-based modelling to examine the fate of founder populations sampled from a larger core population containing a genetic load. Analysis of the effect of various load and population parameters reveal that a genetic load can dramatically reduce the establishment probability of small populations, across a wide range of parameter space. A sterile effect is substantially more effective than a lethal effect, but X-linkage has minimal benefit over an autosomal load. Founder population extinction is readily seen with less than one hundred loci when other load and population parameters are constrained within realistic ranges. Our findings suggest that driving a genetic load into a population may be a means of making that population less invasive and easier to contain and eradicate.