The best way for a driver with a DUI conviction to get a lower insurance rate is to shop around. Some insurers offer better high-risk driver rates than others. And even if a good driver discount no longer applies, there may be other discounts available to the driver. Examples of auto insurance discounts a driver may still be able to take advantage of include: Multiple driver discounts, or Multiple policies with the same insurer (such as home, fire, umbrella, etc.).