Elliott and Müller (2007) (EM) provides a method to construct a confidence set for the structural break date by inverting a locally best test statistic. Previous studies show that the EM method produces a set with an accurate coverage ratio even for a small break, however, the set is often overly lengthy. This study proposes a simple modification to rehabilitate their method. Following the literature, we provide an asymptotic justification for the modified method under a nonlocal asymptotic framework. A Monte Carlo simulation shows that like the original method, the modified method exhibits a coverage ratio that is very close to the nominal level. More importantly, it achieves a much shorter confidence set. Hence, when the break is small, the modified method serves as a better alternative to Bai's (1997) confidence set. We apply these methods to a small level shift in post-1980s Japanese inflation data.