Tesla has promised to tweak the Model S to protect against head contact on the steering wheel in a small-overlap crash.

The Tesla Model S and BMW i3 have surprisingly failed to qualify for the Insurance Institute for Highway Safety's Top Safety Pick awards.

Tesla has touted the Model S as the safest vehicle on the road, achieving an alleged "5.4 stars" in the National Highway Traffic Safety Administration's New Car Assessment Program. The company suggests a lack of engine in the front allows for a superior crumple zone to absorb energy in frontal crashes.

The Model S earned 'good' ratings in all IIHS crashworthiness evaluations, except the challenging small-overlap test that is not included in the government assessments.

"Despite lengthening the side curtain airbags to improve small overlap protection in the Model S, Tesla ran into problems in the test when the safety belt allowed the dummy's torso to move too far forward," the IIHS said in a statement. "That allowed the dummy's head to hit the steering wheel hard through the airbag."

Dummy measurements indicated a risk of injuries to the head and lower right leg in a similar real-world crash scenario.

"The ratings for the Model S apply to 2016 and 2017 cars built after October 2016," the institute added. "Tesla says it made a production change on Jan. 23 to address the head-contact problem, and IIHS will test the updated vehicle for small overlap protection as soon as it can be delivered."

The IIHS evaluations also gave the Model S P100D variant an 'acceptable' rating for roof strength, despite acing the NHTSA trial and even breaking the government's crush test equipment.

Tesla is also said to be working on new headlights after the Model S received 'poor' ratings for all available lighting configurations. The IIHS will reevaluate the new lights when they are available.

The Model S results will undoubtedly attract the most attention in the latest IIHS crash tests, but the BMW i3 also faltered with an 'acceptable' mark in the head restraint and seat evaluation.

"BMW clearly thought a lot about safety when designing the i3," said IIHS research chief David Zuby. "It's a shame that it missed the mark on head restraints, which is something most of today's vehicles get right. Among small cars, the i3 is the only 2017 model that doesn't earn a good rating."

The IIHS points out that a few plug-in hybrid models earned Top Safety Pick Plus awards including the Chevrolet Volt and Toyota Prius Prime. The institute has not yet put the Chevy Bolt through the trials.