Mathematical model indicates SARS-CoV-2 variants that combine enhanced transmissibility with the ability to escape immunity cause more infections than variants with either trait alone. Understanding which type of variants are most likely to increase infections and pandemic severity could help researchers and public health officials interpret the significance of novel and existing variants and design tailored public health responses for various scenarios based on a variant's characteristics. In the case of Delta-like variants, vaccination is predicted to be highly beneficial because vaccinations would prevent a greater number of cases that a more transmissible virus would potentially cause, and because the milder nature of breakthrough infections should substantially reduce overall mortality.