Majority of epidemics eradication programs work in preventive responsive way. The lack of exact information about epidemiological status of individuals makes responsive actions less efficient. Here, we demonstrate that additional tests can significantly increase the efficiency of "blind" treatment (vaccination or culling). Eradication strategy consisting of "blind" treatment in very limited local neighborhood supplemented by extra tests in a little bit larger neighborhood is able to prevent invasion of even highly infectious diseases and to achieve this at a cost lower than for the "blind" strategy. The effectiveness of the extended strategy depends on such parameters as the test efficiency and test cost.