Experts within gifted education have advocated for the use of local norms when selecting students for gifted programs, instead of national-level norms. Local norms compare students to their immediate peers to identify gifted students and are believed to produce a more diverse gifted program. However, district integration limits the ability of local norms to diversify gifted programs, a fact that has been almost completely overlooked in gifted education scholarship. Through a simplified example, we show that local building-level norms are best at diversifying gifted programs when schools are highly segregated. Conversely, when achievement gaps are present and a uniform admissions cutoff is applied, building-level norms in highly integrated schools produce highly segregated gifted programs. In short, the use of building-level local norms trades one form of segregation for another. Implications and recommendations for gifted education and beyond are explored. A preprint version of this article is available at https://psyarxiv.com/nemch/.