This paper proposes to construct the confidence sets for the date of a one-time structural change using point optimal tests. As considered by Elliott and Müller (2007), we first construct the tests for the break date that maximize the weighted average of the power functions. The confidence sets are then obtained by inverting the test statistics. By carefully choosing the weights, we show by Monte Carlo simulations that the confidence sets based on our methods have an accurate coverage rate while the length of our confidence sets is shorter than those proposed in the literature.