Does Jeep have a design problem?

Ew? Maybe.

FORTUNE — The debut of Jeep’s 2014 Cherokee has been anything but ideal. Shortly, after a blog released blurry pictures of the new model rolling off the assembly line in February, the automaker rushed to confirm the design was real — and put out crisp, press-friendly photos. But the polarizing new look didn’t get the manicured auto show launch and media roll-out planned.

The reception wasn’t exactly warm. A post about the leak on Autoblog quickly generated over 1,000 comments, many of them negative. Jeep aficionados on Twitter lamented that the new model wasn’t worthy of the Cherokee name and compared its front facia to a “creepy anime clown face.” (Of course, some praised the vehicle too.) In an interview with Wards Auto, Chrysler design chief Ralph Gilles defended the controversial shape, telling the publication, “There are certain things this new styling has to respond to. I personally see a very cool DNA strain going back to the Grand Cherokee.”

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So is the new Jeep Cherokee ugly? Well, it’s certainly … different. Its new nose looks a little like those found on Jeeps past. Gone are the iconic circular headlamps. In their place: sharply slanted slits. The signature seven-slot grille? Instead of standing upright, it is creased in the middle, folding over the top of the hood as if an elephant sat on the front of it mid-safari.

A lot is riding on the Cherokee. Jeep replaced the previous version in 2002 with the smaller Liberty. According to Ward’s AutoInfoBank, the company sold a record 171,212 units in the U.S. that year. A decade later, that figure had fallen to just 75,482. In contrast, Honda’s (HMC) competing CR-V outsold the Liberty three to one last year. According to sales figures release Tuesday, overall Jeep sales were up 35% month over month in March, but year-over-year sales dropped 13% thanks in large part to the end of Jeep Liberty production.

Now the company is trying to meet rising fuel economy standards — thus the more aerodynamic styling. (The current Liberty achieves 22 miles per gallon on the highway; the new Cherokee should get 31 miles per gallon under similar conditions.) More importantly, Chrysler needs Jeep to become a truly global brand. The new design is, in part, an attempt to appeal more broadly to markets outside the U.S. The Cherokee will be built in Toledo, Ohio and exported to China and some 150 other countries.

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In many ways, Jeep’s problem is a desirable one to have. It has an iconic brand — brimming with the so-called brand equity automakers are so keen to create. Even poorly reviewed extensions of its lineup, such as the ill-fated Jeep Compass, haven’t done much to ding that. A Jeep is still a Jeep. The question is, how can Chrysler broaden Jeep’s appeal without alienating a rabidly loyal fan base or undermining its strengths?

Few have managed that feat. General Motors’ (GM) Buick is known as a ride of choice for the elderly mostly because only older consumers can remember the last time the brand was cool, the 1950s. Ford’s (F) Lincoln division, which is attempting to revive itself, suffers from a similar problem. British luxury brand Jaguar, meanwhile, faltered badly because it held onto its iconic design language far too long.

Old and new done right.

Porsche may be the best example. Much like Jeeps are synonymous with off-roading, Porsche cars are known for a singular purpose: driving fast. The German company’s designs have — mostly — shared strong characteristics, including rounded headlamps as well as the unmistakable slope of the front hood. At the New York Auto Show, currently taking place, I found it striking to see the similarities between a vintage 911 near a next-generation Cayman S. (For evidence, see photo above.)

But the best case study may be a long-gone brand: Hummer. GM’s larger-than-thou heavy SUV began to contemplate life beyond the man’s man demographic in 2008. The company unveiled its Hummer HX concept at the North American International Auto Show in Detroit that year. This Hummer would have been nearly a foot and a half shorter than its then-smallest vehicle and as much as 50% more fuel-efficient. The concept, which was due around 2010, never saw the light of day as the financial crisis doomed the brand. Rather than an apostasy of the Hummer nameplate, the HX carried over the rugged appeal of its larger cousins while achieving new goals including fuel efficiency.

With so much riding on the Cherokee, Jeep executives might do well to study it.

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