(FORTUNE Magazine) – Barry Randall thinks he's found a way to do what many call impossible: make successful long-term investments in dot-coms--that genus of company that led the world on a thrilling if ultimately dispiriting ride not so long ago. Randall, who runs U.S. Bancorp's First American Technology fund (FATCX), led that broad-based tech portfolio to an impressive 56% return last year. But the Minneapolis manager also oversees investments for a few rich clients--and here the focus has been nothin' but Net. In early 2002, at the request of two big investors, Randall crafted a portfolio of ten Net stocks that they could "forget about for 20 years." The point was to create a nest egg for the grandchildren while minimizing taxable trading. So Randall asked himself, "What is everlasting?" And it wasn't a "patent portfolio," he concluded. "It wasn't management--it was basically a business model that was robust enough to withstand stupid managers or unexpected external events."

That answer led him to several online service companies that met key criteria: Their inventory--mostly information--had to be gathered online, and their customers had to need no other software than a browser to do business. Randall also looked for firms with growing revenues and positive operating cash flow.

No surprise, half the companies on his list were household names--Amazon.com, eBay, Internet ad manager Doubleclick, TMP Worldwide (now split in two, including job-lister Monster Worldwide), and Yahoo. Far more exciting is that Randall found a handful of smaller unknowns as well--dot-coms that could turn into tomorrow's Amazons and eBays (see table), like @Road, which uses the Net to help companies manage delivery and logistics; CoStar Group, a huge database of records for the real estate industry; TALX, an online job-reference-checking company; and Websense, which maintains and sells a list of off-limit websites for businesses that want to restrict workers' on-the-job surfing. He later added Concur Technologies, which offers companies web-based expense management for travel and entertainment. Almost all his picks generate cash and bottom-line profits.

When Randall talks about those companies' "frictionless" business models, he sounds a lot like besotted web investors of five years ago. But the former equity analyst says several crucial things have changed. For one, most bad dot-coms have been winnowed out. Poorly conceived me-too Internet companies like online jeweler Ashford.com dropped away, but @Road is a completely different company, Randall says. "Nothing like it ever existed before, yet @Road's Internet service can now be provided to tens of thousands of business customers--tracking delivery trucks, optimizing the routes they travel, and minimizing downtime." When he put the portfolio together in 2002, the company's revenue growth already "clearly indicated they had something people wanted," he explains. While @Road burned through $40 million in 2000, today it generates cash.

Concur has likewise grown up. It used to simply sell T&E software outright but is changing to a subscription model. While revenues declined slightly in the fourth quarter as the company booked more long-term sales, gross margins and cash flow were up. CoStar Group, too, shows improving cash flow. "Tech is enabling a kind of information gathering that was never before possible in real estate," says Randall.

So if this new breed of web company is such a sure thing, why doesn't he invest his mutual fund in the same stocks? Randall holds only Amazon and Concur in the First American fund. He says he pays little attention to stock fluctuations in his set-and-forget portfolio but doesn't have that luxury in the mutual fund, which must make steady returns in a world where many factors other than a company's prospects affect its stock.

But who knows? This luxury might soon pay for itself: Randall's Internet services portfolio was up 110% in 2003.