Many viral infections can be prevented by immunizing with live, attenuated vaccines. Early methods of attenuation were hit-and-miss, now much improved by genetic engineering. However, even current methods operate on the principle of genetic harm, reducing the virus's ability to grow. Reduced viral growth has the undesired side-effect of reducing the host immune response below that of infection with wild-type. Might some methods of attenuation instead lead to an increased immune response? We use mathematical models of the dynamics of virus with innate and adaptive immunity to explore the tradeoff between attenuation of virus pathology and immunity. We find that modification of some virus immune-evasion pathways can indeed reduce pathology yet enhance immunity. Thus, attenuated vaccines can, in principle, be directed to be safe yet create better immunity than is elicited by the wild-type virus.