When using cognitive tests, personnel selection practitioners typically face a trade-off between the expected job performance and diversity of new hires. We review the increasingly mainstream evidence that cognitive ability is a multidimensional and hierarchically ordered set of concepts, and examine the implications for both composite test validity and subgroup differences. Ultimately, we recommend a strategy for differentially weighting cognitive subtests (i.e., second-stratum abilities) in a way that minimizes overall subgroup differences without compromising composite test validity. Using data from 2 large validation studies that included a total of 15 job families, we demonstrate that this strategy could lead to substantial improvement in diversity hiring (e.g., doubling the number of job offers extended to minority applicants) and to at least 8% improvement in job offers made to minority applicants, without decrements in expected selection quality compared to a unit-weighted cognitive test composite. Finally, we conduct a sensitivity analysis to examine whether the technique continues to perform well when applied to applicant pools of smaller size. We discuss prerequisites for the application of this strategy, potential limitations, and extensions.