DETROIT — Two luxury electric vehicles — the Tesla Model S and the BMW i3 — fell short of getting the highest safety ratings in new crash tests by the insurance industry.

The Insurance Institute for Highway Safety tested 2017 models of both vehicles. Neither earned the institute’s “Top Safety Pick” award, which is given to vehicles that get the highest rating in five different crash tests and offer a crash-prevention system with automatic braking. To get a highest “Top Safety Pick-Plus” designation, vehicles must meet all of those criteria and have good headlights.

In the 2017 model year, 38 vehicles have won the “Top Safety Pick-Plus” designation, including two plug-in hybrids: the Toyota Prius Prime and the Chevrolet Volt. But no all-electric vehicles are on the list. The institute hasn’t yet tested the all-electric Chevrolet Bolt, which went on sale at the end of 2016.

Tesla’s Model S, an all-electric luxury sedan that starts at $72,500, earned good ratings in four of the institute’s five tests, including a side impact test and a head restraint test. But it earned a lower rating in a small overlap frontal crash test, which replicates what happens when the front corner of the car collides with a tree or telephone pole at 40 miles per hour. The Tesla’s safety belt allowed the crash dummy to move too far forward and it hit its head on the steering wheel.

The institute said Tesla made a production change this month to address the problem, so the car will be tested again. The Model S has earned the highest ratings on U.S. government crash tests, but IIHS performs different tests.