We examine the location properties of a conditional selective confidence interval constructed via the polyhedral method. The interval is derived from the distribution of a test statistic conditional on the event of statistical significance. For a one-sided test, its behavior depends on whether the parameter is highly or only marginally significant. In the highly significant case, the interval closely resembles the conventional confidence interval that ignores selection. By contrast, when the parameter is only marginally significant, the interval may shift far to the left of zero, potentially excluding all a priori plausible parameter values. This "location problem" does not arise if significance is determined by a two-sided test or by a one-sided test with randomized response (e.g., data carving).