A leather handbag by Michael Kors. (Martin Divisek/Bloomberg)

Michael Kors and Coach are keenly aware of their central problem in the U.S. market. They are ostensibly luxury brands, selling an aspirational lifestyle — and yet you can find their handbags at mid-tier, everyman department stores, and you can often buy them on the cheap thanks to promotions.

The deals eat away at their cachet, not to mention their profit margins.

And so each company announced a bold move this week that they hope will help them get their aura of exclusivity back. Coach said it plans to pull its products out of more than 250 department stores, a move that reduces its presence in such locations by 25 percent. Meanwhile, Michael Kors said Wednesday that it is not pulling out of specific stores but is reducing the inventory it provides to department stores and, starting in February, is demanding to be excluded from storewide promotions and coupons.

With these actions, the handbag giants are stepping back from department stores, trying reduce their exposure to the deals merry-go-round and, in turn, put more pricing and messaging control back in their own hands.

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In the most recent quarter, Kors chief executive John Idol said department-store promotions were “causing us difficulties” in the brands’ own specialty stores because managers felt pressured to match the prices that shoppers were seeing elsewhere at the mall.

Plus, Idol told investors on a Wednesday conference call, “We think it’s creating confusion in the consumer’s mind relative to the value of the Michael Kors brand when it’s being seen so often on sale.”

Victor Luis, Coach’s chief executive, offered a similar analysis to investors on Tuesday when he explained why the accessories maker was pulling back from department stores. While he liked that those kinds of retail locations offer the opportunity for people to try the Coach brand for the first time, he felt their promotional strategies were “generating confusion” relative to what Coach is trying to do in its own stores.

Kors said its goal in the United States and Canada is to sell fewer items, but at higher price points. (Their plans for major growth in the Asian market and the men’s business, executives say, should also help offset the lost sales.)

That kind of talk probably sends a chill down the spines of department store executives because it raises a critical question: If these luxury brands decided to reduce their business with department stores, could other apparel and accessories makers follow suit? If they were to do so, it could turn an already-troubled segment into a fashion backwater. Plus, many big-name department stores in the United States,  such as Macy’s, Bloomingdale’s, Nordstrom and Lord & Taylor, have little or no physical retailing presence overseas, meaning they’re not well-positioned to be a part of the growth potential that brands like Kors see in international markets.

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Department-store discounting is hardly the sole culprit of Kors’s and Coach’s struggle to retain exclusivity. Kors has been adding specialty stores at a breakneck pace, bringing its fleet to 771 locations across the world, compared with 550 last year. How elite can a chain really feel when it is a fixture in hundreds of suburban shopping malls? And Coach has notoriously suffered from leaning too heavily on its outlet stores for growth, a move that hurt the brand with prestige-minded customers.

Coach is further along than Kors is in its bid to reestablish itself as an upscale brand. The company just posted an increase in sales at its existing North American stores for the first time in more than three years. And some 40 percent of handbag sales this quarter were pieces that cost more than $400; last year, those items made up only 30 percent of sales.

Meanwhile, Kate Spade — the other member of the triumvirate of accessible luxury handbags — has not announced a pullback from department stores. And yet executives also spoke of trouble recently in dealing with promotions. The company said last week that in its own stores, it would push full-price items and save its discounts for special sale events, perhaps cutting even deeper during those periods. The retailer already has cut back on flash-sale events this year, holding only about one-third as many as it once did.