I buy the collision damage waiver when I rent a car because I don’t want my insurance company to know if I’m in an accident. What if I hit another vehicle and it’s my fault?G.T., Albany, N.Y.

The collision damage waiver (CDW) covers damage to the rental car, but it doesn’t cover liability if you injure someone or damage another car or property. The rental car company may automatically provide a small amount of liability coverage. But if it’s not enough, your own auto insurance will generally cover you up to your policy’s liability limits if you rent a car in the U.S. or Canada (but usually not in other countries), says Bill Wilson, an insurance educator and founder of InsuranceCommentary.com, an industry blog. If you don’t want your insurer to cover an accident that’s your fault, you will have to buy supplemental liability coverage from the rental car company in addition to the CDW. For example, Enterprise charges $10 to $15.50 per day for $1 million in coverage.

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Many renters turn down the CDW, which can cost $9 to $25 per day, because their own policy covers damage to the rental car and many credit cards pay the deductible. But buying the CDW eliminates the hassle of filing a claim with your insurer (which could lead to a rate hike). It also covers costs your insurer or credit card company may not pay, such as loss of use and diminished value charges.