DETROIT — Six of 12 small cars performed well in front-end crash tests conducted by an insurance industry group, but some popular models fared poorly in the safety evaluations.

Only the two-door and four-door Honda Civic models earned the top rating of “good” in the tests done by the Insurance Institute for Highway Safety. The Dodge Dart, Ford Focus, Hyundai Elantra and the 2014 Scion tC got “acceptable” ratings.

But popular models such as the Chevrolet Cruze and Sonic and the Volkswagen Beetle got “marginal” ratings, while the Nissan Sentra and the Kia Soul and 2014 Kia Forte each were rated “poor.”

The group didn’t test the Toyota Corolla because a new version is coming out in the fall. The Corolla is the No. 2 selling small car in America, behind the Civic. The IIHS ratings are influential because many auto shoppers find them while researching vehicles on the Internet.

The market for small cars is one of fastest-growing in the U.S. Automakers have made the cars quieter and more refined as people who want good gas mileage turn to compacts and subcompacts. So far this year, Americans have bought more than 1.8 million new small cars, up 12 percent over a year ago, according to Autodata.

The cars were rated for their performance in the insurance institute’s “small overlap” test of crashes that cover only 25 percent of a vehicle’s front end. These tests, added to the IIHS’s evaluations last year, are forcing automakers to bolster the front-end structure of all cars in order to avoid bad publicity from a poor performance.

The IIHS tests are more stringent than the U.S. government’s full-width front crash test.