Whereas complexity is usually perceived as a negative factor opposing safety of critical infrastructures, in this paper we claim that complexity can be positively exploited to relax safety. For this purpose, we consider an infrastructure as a complex adaptive system (CAS). To ground our claim three case studies will be conducted on critical computer infrastructures. In the first case study, a large trusted computer network relapses after a disaster or attack into an anarchistic hardly trusted network. In the second case, critical nodes in a large trusted computer network suffer from Denial of Service attacks. In the third case the Internet is suffering from ISP routing oligopolies. In all the cases we will show how CAS resolves the problems.