Recent research has identified significant performance hurdles that sound gradual typing needs to overcome (Takikawa et al. 2016). These performance hurdles stem from the fact that the run-time checks gradual type systems insert into code can cause a lot of overhead. We propose a small sacrifice in flexibility that enables us to implement efficient checks. We formalize the core of a nominal object-oriented language that fulfills a variety of desirable properties for gradually typed languages, and present evidence that an implementation of this language suffers minimal overhead even in adversarial benchmarks identified in earlier work, while achieving good overall performance.