If you’re relying on a vehicle-history report when buying a used car, you could be making a costly mistake.

Carfax, AutoCheck, and other car-history report services can be useful for what they tell you. But it’s what they can miss that’s the problem.

In a recent Consumer Reports investigation, we obtained history reports for dozens of seriously damaged vehicles being sold on eBay Motors and other Web sites. Some of the reports came back “clean” even though the vehicles were being displayed with photos showing the extensive damage, along with descriptions of the problems and vehicle identification numbers.

For example, a smashed 2007 Acura MDX, described on one auction site as a “ROLLOVER; ALL OVER,” got a clean report from Carfax and a rating of 89 out of 100 from AutoCheck.

If you’re buying a used car, by all means, take a look at a vehicle-history report, especially if it’s being provided at no cost to you by a dealer or private seller, as is often the case. But don’t stop there. Drive and carefully inspect the vehicle. Most important, have it checked out by qualified mechanic, preferably one with auto body experience. A thorough inspection is critical, no matter how new the car is or how clean it looks, or even if it’s covered by a warranty.

See our full car-history report investigation, including some stunning photos of wrecked cars that came back with clean titles.

—Anthony Giorgianni