A variety of mitigation strategies have been employed against the Covid-19 pandemic. Social distancing is still one of the main methods to reduce spread, but it entails a high toll on personal freedom and economic life. Alternative mitigation strategies that do not come with the same problems but are effective at preventing disease spread are therefore needed. Repetitive mass-testing using PCR assays for viral RNA has been suggested, but as a stand-alone strategy this would be prohibitively resource intensive. Here, we suggest a strategy that aims at targeting the limited resources available for viral RNA testing to subgroups that are more likely than the average population to yield a positive test result. Importantly, these pre-selected subgroups include symptom-free people. By testing everyone in these subgroups, in addition to symptomatic cases, large fractions of pre- and asymptomatic people can be identified, which is only possible by testing-based mitigation. We call this strategy smart testing (ST). In principle, pre-selected subgroups can be found in different ways, but for the purpose of this study we analyze a pre-selection procedure based on cheap and fast virus antigen tests. We quantify the potential reduction of the epidemic reproduction number by such a two-stage ST strategy. In addition to a scenario where such a strategy is available to the whole population, we analyze local applications, e.g. in a country, company, or school, where the tested subgroups are also in exchange with the untested population. Our results suggest that a two-stage ST strategy can be effective to curb pandemic spread, at costs that are clearly outweighed by the economic benefit. It is technically and logistically feasible to employ such a strategy, and our model predicts that it is even effective when applied only within local groups. We therefore recommend adding two-stage ST to the portfolio of available mitigation strategies, which allow easing social distancing measures without compromising public health.