Like many rental car customers, my husband and I declined the expensive insurance offered at the counter.

We knew we were covered through our auto insurance provider. Additionally, the credit card we use covers rental cars. In my mind, if we got into an accident, I would just use the coverage offered by the credit card company.

But during our recent vacation, we came out one morning to climb into our minivan and found that the bumper had been hit, or so we thought.

In anticipation of filing a claim with the credit card company, a wave of panic set in as we realized that the coverage was “secondary,” meaning that we had to go through our personal car insurance company first. And you know what that means. In all likelihood — our fault or not — the claim could result in a premium increase.

It turns out that lots of people don’t know about the secondary-coverage catch. Sixty-five percent of rental car customers are unaware that credit card insurance often kicks in only when damages can’t be first recovered from their auto policy, according to a YouGov survey commissioned by InsureMyRentalCar.com, a provider of rental auto insurance.

Now, here’s another twist in my minivan mayhem. When I looked carefully at the damage, I discovered it had been there all along. I was feeling across the cracks — there were two — and I discovered black duct tape on the backside of the bumper. Because of the hot temperatures — we were vacationing in Florida — the tape had split. The minivan hadn’t been hit at all during our rental. I hadn’t detected the cracks when we first picked up the vehicle because it was a dark color and, once taped up underneath, there were only hairline fractures. We never saw them.

Another survey commissioned by InsureMyRentalCar.com found that 23 percent of rental customers found damage on the car that was not highlighted on their checkout sheets. Nearly 29 percent of customers said they were concerned that a rental company would try to charge them for damage that they didn’t cause.

I always take time to inspect the rental car and to snap photos of any damage I find, no matter how small. Once, when I pointed out a small scratch, a rental agent said: “Oh, don’t worry about that. We won’t charge you for something like that.”

“No, sir,” I said. “Please record the scratch on my paperwork.”

I did the same thing for this rental. I noticed some scratches, took pictures and made a notation on my rental agreement.

InsureMyRentalCar.com reported that 4 percent of rental customers think they were wrongly accused of damaging a car. Although 64 percent of people said they always check for preexisting damage, only 19 percent take a photo as proof when there is something wrong. And people often neglect to check the condition of the wheels and tires.

Here’s some advice after my rental scare:

●Double-check ahead of time what your personal auto policy covers for a rental, including whether you’re covered for “loss of use,” which is a charge you could have to pay while the vehicle is being repaired.

●Read your credit card agreement. Really pore over the conditions related to rental cars. I should have read more carefully.

●Pay attention to the exclusions and restrictions. With our card, the secondary coverage provides only collision damage to the rented vehicle. It does not cover injuries to us or anyone else. It doesn’t cover damages to other vehicles or property. And not all vehicle types are covered. My card does not cover any vehicles with a manufacturer’s suggested new retail price of $50,000 or more.

●The secondary insurance might not kick in if you rent the vehicle for longer than a certain number of days.

●Be sure to take pictures when you return the car.

●If you don’t want to risk an auto insurance claim, consider getting primary coverage from a third-party company. Shop around for rates. InsureMyRentalCar.com offers waivers for loss and collision damage starting at $17.50 per trip.

We won’t have this scare again. We now have premium rental coverage from American Express. It’s $24.95 per rental period (not per day). If there is a theft or damage to the car, we can file that claim with the company as a primary provider. And there is no deductible.

For more tips, go to www.insureuonline.org and search for “car rental considerations.”

There’s so much to think about when you are planning your vacation that it’s easy to speed through agreements, especially if you think you know something. But slow down. Do your homework. Even those of us who are typically meticulous about checking things can overlook important details that can crash your trip.

Readers may write to Michelle Singletary at The Washington Post, 1150 15th St. NW, Washington, D.C. 20071 or send her an e-mail at michelle.singletary@washpost.com. To read previous Color of Money columns, go to http://wapo.st/michelle-singletary.