You've just gotten over that queasy feeling after giving the car keys to your newly minted teenage driver, then you get the punch to the gut: Your insurance bill arrives.

On average, parents can expect their auto premiums to double when adding a teenage son to their policy and jump 50 percent or more when adding a teen daughter, according to the Insurance Information Institute. That doesn't include the hit from adding another car if you decide junior needs one of his own.

It's not hard to understand why coverage is so costly. Teenagers made up 4.7 percent of drivers in 2004 but accounted for 14 percent of all accidents -- the highest accident rate of any age group, according to the National Safety Council. Teens also are four times more likely to be killed in a car crash than drivers over 25.

"Sixteen-year-olds are especially dangerous drivers," said insurance institute Vice President Carolyn Gorman. "They lack experience and have a tendency to think of themselves as immortal and are enthralled by a feeling of independence when they get behind the wheel."

If your teenager is still driving under a permit, insurers often won't charge for coverage. Even so, be sure to contact your agent right away when your teen gets a regular license, said Randy Rohrbaugh, deputy commissioner at the Pennsylvania Department of Insurance.

Some policyholders try to save money by failing to claim teen drivers, hoping that an accident will be covered by the policy's permissive user clause, Mr. Rohrbaugh said. That clause provides coverage when people lend their cars for occasional use to a friend or neighbor.

"Consumers who try to get away with this should not. This is insurance fraud," he said.

"You're setting yourself up to have the insurer deny a claim."

Still, there are a number of ways to minimize the sting when adding a teenager to your policy.

Many insurers offer premium discounts of 10 percent to 20 percent for good students, typically those who maintain a "B" average or better.

"Insurers can see a link between students who take their school responsibilities seriously and driving responsibilities seriously as well," the insurance institute's Ms. Gorman said.

Discounts of up to 15 percent typically also are offered for teens completing a formal driver's training course, similar to discounts often available for seniors willing to take a driver improvement course.

Be sure to ask insurers about other special breaks available for teens.

For example, at State Farm, the state's largest auto insurer, drivers under age 25 who meet certain eligibility requirements and complete the Steer Clear safe driver program can earn up to 15 percent off their annual premium, or the equivalent of up to $190. The program involves watching a video, reading a safe-driving magazine and keeping a driving log during 30 driving trips.

Here are some other money-saving strategies to keep in mind:

Save during school. If your son or daughter is going away to school and leaving the car at home, let your insurer know. You'll get a discount for the time your child isn't around to drive the car.

Share cars with your teen instead of buying a third vehicle. Insurers typically match the number of licensed drivers to the number of vehicles in a household. For a couple with more than two cars, adding a teenage driver can be a double whammy, since the teen likely will be considered the primary operator of one of the vehicles instead of an occasional driver, a less costly designation.

If you decide to buy, choose a vehicle that's insurance-friendly. Premiums can vary by hundreds of dollars depending on the model's injury, collision and theft loss history. "If Mom is going to buy a teenager a new Toyota Celica, the kind street racers like, it will have a higher effect [on the insurance premium] than if she buys a Ford Focus," the insurance department's Mr. Rohrbaugh said. Check a vehicle's insurance rating with your agent.

Shop around. Adding a teen to your policy is a good time to compare prices among a number of insurers. For sample rate comparisons of leading insurers in Western Pennsylvania and an overview of auto insurance coverage, visit www.insurance.state.pa.us. Consider getting a quote from at least one direct insurer, such as Geico or Amica. These companies lower overhead costs by selling directly instead of through agents.

Not too far down the road, you may be able to enjoy a sizable discount for installing a device in your teen's car that uses global positioning to track the vehicle's speed, mileage, driving patterns and other safety-related issues, such as whether your teen's seat belt is fastened.

Insurers are starting to experiment with offering such discounts, and also for less sophisticated "black box" type recording devices, but Mr. Rohrbaugh said the breaks currently aren't available to policyholders in Pennsylvania because of public backlash over privacy concerns.