By Jennifer Smith, The Wall Street Journal

Companies that once regularly hired the pricey titans of the legal business are sending more work to smaller, cheaper firms—and not just for routine jobs.

Over the past three years, midsize law firms with 201-500 lawyers have nearly doubled their share of big-ticket litigation, to 41% from 22%, of the work that generates more than $1 million in legal bills, according to a new analysis set to be released Tuesday.

The biggest firms—with more than 750 lawyers—are losing ground. During the same time period, their share of overall legal billings dropped to 20% from 26%, while midsize firms increased their market share to 22% from 18%. The figures are based on an analysis of $10 billion in legal fees by CounselLink, a legal software provider and a division of LexisNexis.

That shift spotlights how clients’ relentless hunt for savings continues to upend a profession in which marquee firms have long dominated lucrative corporate work.

“The larger the firm the higher the cost,” said Don H. Liu, general counsel for Xerox Corp. While he uses elite law firms for critical transactions, he helps keep the company’s legal bills in check by sending other work to smaller law firms in St. Louis and other low-cost locations. “Big law firms don’t have a monopoly on talent,” he says.

General counsel at many companies have become smarter shoppers since the economic downturn in 2008, when clamping down on legal costs became a necessity.

Corporate law departments face continued pressure to keep the bills down. Switching from a big firm with expensive offices in New York or Los Angeles to a midsize shop with 500 or fewer lawyers can yield significant savings, in-house lawyers say.

A partner who specializes in mergers and acquisitions might cost anywhere from $700 to $1,000 an hour in New York or London to “around $500 an hour” in the Midwest, according to Nick Sayeedi, the general counsel for Blockbuster LLC. “And many of these people have come from the big firms and have similar expertise.”

He added that some in-house lawyers resent having big law firms continue to boost their hourly rates 5% to 10% at a time when some companies are struggling, with revenue growing at a slower rate.

But quality matters too. “This is an art, and you can’t just treat obtaining legal services like you’re going to the lowest common denominator,” said Brackett Denniston, general counsel at General Electric Co., which has long evaluated law firms by looking at both quality and price.

Indeed, corporations still hire name-brand firms for the most crucial matters—a multibillion-dollar acquisition, for example, or a class-action lawsuit that puts a company’s reputation on the line.

Many of the largest U.S. law firms also remain the most profitable, despite the incursions into market share. Losing out on some lower-end work isn’t necessarily a big blow to elite New York firms or those with armies of lawyers in major U.S. cities—as long as they continue to land the most sophisticated and lucrative assignments. “The losers are the big firms that aren’t migrating to high-rate work,” said legal consultant Kent Zimmermann, who is based in Chicago.

But the pool of such work is shrinking as clients grow increasingly comfortable with sending complex work to smaller or lesser-known firms. “Firms further down the food chain are getting more of that high-rate work than they used to,” Mr. Zimmermann said. “That’s the result of a chain reaction that started in 2008 and continues today.”

Small and medium-size firms face their own competitive pressures. Despite the increased flow of work down market, many of them have opted to grow through mergers with other firms. Such combinations can increase a firm’s reach and, potentially, its revenue if existing clients opt to send more business its way. Big firms also enjoy some economies of scale and can offer bigger paychecks to lure talented lawyers from smaller shops.

Many companies like to hire a mix, retaining big international firms for complex, cross-border work but hiring small firms and even solo practitioners for matters such as patent prosecution that don’t require such a deep bench.

Ronald S. Milstein, general counsel for Lorillard Inc., said the tobacco company uses Hughes Hubbard & Reed LLP, a well-known New York law firm, to handle corporate work and national product-liability litigation. But he hired a smaller regional firm, Adams & Reese LLP, to do extensive work on about 4,500 state and federal civil litigation cases pending in Florida and to work with the larger national firms that Lorillard also employs.

“Not everything is a bet-your-company kind of case, and not every case warrants the big guns from New York,” Mr. Milstein said. “Smaller firms—they want you more, they value you more.”

Some companies have always shopped around for legal services, but before the recession, general counsel would often hire well-known law firms as a sort of insurance policy to reassure nervous boards and investors, particularly during big transactions. “You can’t get criticized for selecting Sullivan & Cromwell,” said Robert S. Marin, general counsel for Panasonic Corp. of North America.

For some chief legal officers, though, the prestige of the individual law firm has become less important than the capabilities of individual lawyers.

Many smaller law firms have partners and attorneys who were trained at the country’s biggest law firms and then left. And clients are increasingly willing to hire those lawyers, according to a recent survey of top legal officers at 88 big companies by AdvanceLaw, a company that helps general counsel at Panasonic, Google Inc. and other companies vet law firms and attorneys.

Nearly three-quarters of those surveyed said they would be less likely to use a “pedigreed” firm for high-stakes matters if they could save 30% of the total bill by hiring a good lawyer from a less-prestigious firm.

Cost isn’t the only part of the equation. Nearly 60% of the general counsel polled by AdvanceLaw said lawyers at the most elite law firms were less attentive to their concerns than those at other firms.

“Sometimes they are responsive,” wrote one respondent, who heads up legal services at a company in the publishing industry, “but in ways that end up being breathtakingly expensive.”