Critics have praised new Cadillacs such as the ATS Coupe. GM's next job: drawing German-luxury-brand loyalists to Cadillac. Source: General Motors.

Here's an interesting conundrum: How do you fix a broken luxury brand?

When General Motors (NYSE:GM) set out to restore its long-tarnished Cadillac brand to global glory, it was clear the first priority was to improve Cadillac's products. Out went the "rolling sofas" of years past, in came new models that combined taut handling and crisp performance with much more upscale interiors. Critics were impressed: The compact ATS sedan was compared favorably to rivals from BMW and Mercdedes-Benz, and the midsize CTS sedan that followed a year later was named Motor Trend's Car of the Year. 

Cadillac had finally arrived as a global luxury player -- or so it seemed. While its latest models seemed almost to out-German the German luxury stalwarts, the Cadillac brand itself still needed work. Market research showed the brand was not drawing much "consideration" from BMW and Mercedes buyers -- in other words, the new Cadillacs weren't making it onto their shopping lists.

While Cadillac had great new cars, it didn't have the cachet to compete with the German brands. 

GM's leaders knew it needed to take aggressive action to change that. In 2013 the company hired longtime BMW executive Uwe Ellinghaus and put him in charge of an ambitious project: turning Cadillac into a respected global luxury brand. 

We had a few minutes with Ellinghaus at the North American International Auto Show in Detroit earlier this month, and we asked him a simple question: How do you fix a broken luxury brand? In this short video, shot on Cadillac's show stand, you can hear what he told us. Check it out, and then scroll down to leave a comment with your thoughts.