A LexisNexis study released Tuesday shows that the nation’s largest law firms—those with at least 750 attorneys—saw their share of outside counsel spending slip in the three-year period that ended on June 30, 2013, while firms with 201–500 lawyers moved in the other direction.

According to the 2013 CounselLink Enterprise Legal Management Trends Report, the country’s 50 largest firms accounted for 20 percent of client fees paid in the United States during the 12 months that ended June 30, compared to the 26 percent share those firms controlled at the same point three years ago.

During the same period, firms the LexisNexis report labels “large enough”—those that, in addition to having 201–500 lawyers, have multiple offices and practices, as well as the ability to meet large corporate legal departments’ needs—saw their share of U.S. legal fees jump from 18 percent to 22 percent. (The report makes no distinctions about whether the firms discussed are members of The Am Law 100 or Second Hundred.)

The report’s principal author, Kris Satkunas, says the reason more clients are shifting work to midsize firms is obvious: Smaller firms offer lower billing rates. What’s more intriguing, Satkunas notes, is the type of work changing hands.

The LexisNexis report found that during the three years in question, firms in the 201-500-lawyer range nearly doubled the number of litigation matters worth on their collective docket worth at least $1 million. Such firms accounted for 22 percent of that work as of June 30, 2010. By June 30 of this year, that figure had surged to 41 percent.

The group’s gains in big-ticket litigation appear to have come at the expense of the nation’s largest firms. The LexisNexis study shows that 50 biggest firms landed roughly 20 percent of the $1 million–plus litigation as of June 30, compared to roughly 30 percent at the same point three years ago.

“The fact that it was [high-fee litigation] that showed that dramatic shift was honestly surprising to me,” says Satkunas. She adds that though many large firms have been moving away from certain types of work—either because it isn’t profitable or because they want to devote their resources elsewhere—large-scale litigation continues to be prized: “The large litigation is work that everybody would like to have, including those larger firms.”

The LexisNexis study isn’t the first in recent months to show the nation’s biggest firms losing ground to somewhat smaller competitors. The Am Law Daily reported in January on a Wells Fargo survey that found Am Law Second Hundred firms slightly outpacing their Am Law 100 rivals in terms of both revenues and net profits in 2012. The American Lawyer’s own financial reporting subsequently showed that Second Hundred firms were more aggressive than their larger counterparts in beefing up their attorney ranks last year, increasing their combined head count 3 percent compared to The Am Law 100′s 0.8 percent uptick.

Another recent report, this one released by TyMetrix in August, tracked hours bought and fees paid by 70 large corporate clients across eight different industries. As The American Lawyer reported at the time, the LegalView Legal Market Index showed Second Hundred firms increasing their hours by 0.1 percent and their fees by 4.6 percent between the first half of 2012 and the same period this year. The Am Law 100, meanwhile, saw its billable hours fall 6.9 percent and its fees drop 4 percent during the period.