Since introduction of search designs by Srivastava (1975), these designs have been constructed by many researchers. There also have been developed some criteria in order to evaluate the search ability of these designs. These criteria are reviewed in this paper. Search designs, which are efficient with respect to search, may be poor in parameter estimation. In this paper, we propose a dual-task criterion to deal with both search and estimation performance of the search designs. The criterion is implied to some designs and the results are given.