Raise Your Deductible
The deductible is the amount you'll have to pay out of pocket in the event of a claim. Once you've met the deductible, the insurance company takes care of the rest. Why on Earth would you want a high deductible? The higher your deductible, the lower your premium will be.
Basically, when you crank your deductible up to $1,000, you're taking a calculated risk. You're banking on the chance that your teen won't get into an accident. If he or she does, a minor accident will be under your deductible, so you won't bother claiming it. A really bad accident will result in such enormous damages that the $1,000 will seem like chump change compared to what the insurance company covers. So raise that deductible, have some very serious talks with your teen about driver safety, and keep your fingers crossed.