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In this paper, we study the problem of minimizing the H2 norm of a given transfer function subject to time-domain constraints on the time response of a different transfer function to a given test signal. The main result of this paper shows that this problem admits a minimizing solution in R~H~2. Moreover, rational solutions with performance arbitrarily close to optimal can be found by constructing families of approximating problems. Each one of these problems entails solving a finite-dimensional quadratic programming problem whose dimension can be determined before hand. These results are illustrated and experimentally validated by designing a controller for an active vision application.