Inspired by Cohen et al. [14, 15] , the aim of the present paper is to explore the effect of such targeted immunization strategies on the course of an epidemic considering a real disease -smallpox-using pessimistic assumptions and suboptimal vaccines. We use computer simulations based on a stochastic transmission model where individuals are connected with each other in two superimposed networks, which allows us to distinguish between close contacts (comprising family members and close friends which can easily be traced) and casual contacts who will be more worrisome in case of an outbreak, because they are more difficult to detect and to be placed under surveillance. For the latter ones, we use a highly skewed network. Our baseline intervention scenario considers case isolation (with a limited capacity) and tracing of close contacts which we combine with a pre-emptive vaccination of highly connected individuals. In our simulations, we identify highly connected individuals by first "asking" a small random fraction of the population to supply the names of their casual contacts. The most frequently mentioned contacts are then offered to be vaccinated. Depending on the simulation scenario, only a fraction of the contacts can be named, or alternatively, only a fraction of the most frequently mentioned contacts can be immunized (this may be caused by combination of a low vaccination eligibility and an imperfect vaccine efficacy). In some of the considered scenarios, highly connected individuals are additionally placed under surveillance for an indefinite duration, so that they can be prevented from spreading the infection.