No major car company has had more difficulties in the U.S. market than global behemoth Volkswagen. VW has struggled as sales fell month after month, while the traditional leaders from Japan and the United States continued to dominate. Also, South Korean brands Hyundai and Kia grew from close to zero a decade ago to real factors. VW has made the start of recovery, though its market share remains small.

Kelley Blue Book (KBB) estimates that VW’s sales will rise 10.5% in June to 55,000, better than any other car company except Fiat Chrysler Automobiles N.V. (NYSE: FCAU), which is expected to grow at the same rate. The American market will rise 5.8%, according to KBB, to 1.5 million. While VW’s recovery rate is impressive, its share of market will be only 3.7%. VW’s sales include its Audi and Porsche brands. Audi often beats Mercedes and BMW in growth rate among German manufacturers.

What has vexed VW as much as anything is that it is the largest car company in the world, by some measures. It has a market share of close to 25% in Europe, and it is among the market leaders in China, the leader in sales among all countries.

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VW still relies on one very successful car to pull its overall sales higher — the much-awarded Golf. Sales of the line are often in the double digits per month. Golf family sales rose 252% in May to 6,308. But VW has to contend with poor sales of it top-selling car, the Jetta line, sales of which fell 7.5% in May to 12,875.

KBB analysts see success beyond June:

Volkswagen Group is another manufacturer poised to report solid growth, thanks to the full model lineup of its redesigned Golf. The Audi brand also is providing a boost with double-digit growth this year, while the overall luxury market is 7.4 percent higher than last year.

The Golf has both two-door and four-door versions.

In a recent analysis of five cars everyone wants this year, the Golf was on the list:

Golf is a bit of an outlier because it’s a replacement model. We include it here because the new one is so damned good. No matter what model you choose — standard Golf, GTI, R, even the e-Golf, you’re getting one of the planet’s best-built, best-handling small cars. We couldn’t say that about the outgoing model.

As time passes, if only VW could add to the Golf, it could contend with the manufacturers that hold the second tier of U.S. sales, companies that include Nissan and Hyundai.

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