Irreducible complexity is a concept developed by Michael Behe to describe certain biological systems. Behe claims that irreducible complexity poses a challenge to Darwinian evolution. Irreducibly complex systems, he argues, are highly unlikely to evolve because they have no direct series of selectable intermediates. Various computer models have been published that attempt to demonstrate the evolution of irreducibly complex systems and thus falsify this claim. However, closer inspection of these models shows that they fail to meet the definition of irreducible complexity in a number of ways. In this paper we demonstrate how these models fail. In addition, we present another designed digital system that does exhibit designed irreducible complexity, but that has not been shown to be able to evolve. Taken together, these examples indicate that Behe’s concept of irreducible complexity has not been falsified by computer models.