Think you have to have an e-commerce presence to succeed in U.K. retail these days? Think again. Some of the winners over the crucial holiday period don’t even sell online.

Although Associated British Foods PLC’s Primark suffered from the warm October—as did its rivals—its domestic sales were miles ahead. It was a similar picture at the U.K. arms of the German no-frills supermarkets, which had a phenomenal Christmas, and variety store B&M European Value Retail SA. None of these stores has a full web offering. Only Aldi has a limited assortment online, covering just wine and non-food items.

The largely disappointing holiday trading updates for the high-street chains have stoked concerns over the future of physical retail. But the discount retailers show that stores are alive and well.

Gadfly has long argued that online sales don’t come for free. For a start, there’s the cost of delivery, which shoppers often don’t fully pay for. Returned goods, meanwhile, are troublesome and expensive for retailers to deal with.

Then, there is the constant investment in facilities to conjure up ever-faster shipping times. Just look at the amount of capital being consumed by the likes of Zalando SE and ASOS PLC.

It’s a similar picture in the United States, where T.J. Maxx is one of the few value retailers to have ventured online. But its prices are higher than Primark’s. And in parent TJX Cos Inc.’s (No. 127 in the Internet Retailer 2017 Top 500) latest fiscal year, it said e-commerce represented just 1% of sales and had an “immaterial impact” on revenue growth.

Discounters underline the fact that retailers can still thrive in a world where more and more shopping is moving online, provided they get back to some basic retailing: having attractive products at prices that customers are prepared to pay.

This means that store environments matter, too. Aldi and Lidl have been improving their supermarkets, for example, by adding fresh bakeries. Though T.J. Maxx (known as T.K. Maxx in Britain) hasn’t yet reported holiday sales, its historical strength suggests that its treasure-hunt-like atmosphere is still a powerful magnet to get shoppers into store.

Amazon.com Inc.’s (No. 1) push into fashion has raised the pressure for value chains to go digital. But they should resist for as long as they can. The economics of e-commerce are not going to improve for the discounters any time soon — they’re already at a disadvantage since the value of the their shopping baskets is smaller because of their lower prices. While they may be losing some shoppers who want the convenience of digital ordering and shipping, they risk hemorrhaging customers if they raise their prices to make online more palatable.

Primark dipped its toe into the e-commerce water five years ago, selling only briefly via ASOS. It wanted to learn — and it did: The experiment convinced it that no other retailer could operate online at its low prices. Today, Boohoo.com PLC is closest to doing that.

Discount chains have other levers they can pull. They can showcase their products on the web without making those sites transactional. Primark, for example, uses social media expertly to communicate with its young, internet-savvy consumers, having more than five million Instagram followers.

Though cheap may be chic right now, when it comes to online, this is one trend that the discounters shouldn’t rush to follow.