The largest U.S. law firms are capturing a smaller portion of legal fees, as corporate legal departments shift work to mid-size firms that offer more flexible billing arrangements, according to a new report by LexisNexis.

The share of U.S. legal fees paid by clients to firms with more than 750 lawyers shrank from 26 percent to 20 percent in the past three years. During the same period, firms with 201 to 500 lawyers saw their portion grow to 22 percent from 18 percent, according to the report, which analyzed more than 2 million invoices that outside law firms billed their corporate clients. The invoices covered more than 300,000 matters valued at more than $10 billion in legal fees.

The shift is even more dramatic with litigation matters — the area that companies have traditionally been willing to shell out top dollar to a large law firm. Over the past three years, the share of fees from high-cost litigation (that cost more than $1 million) that went to mid-size firms (201-500 lawyers) nearly doubled from 22 percent to 41 percent. Meanwhile, the share of such fees that went to large firms (750 or more lawyers) dropped to 19 percent from 32 percent.

Mid-size firms are also much more likely to use alternative fee arrangements to charge clients, the report found. Firms with 201 to 500 attorneys used such fee arrangements in about 6 percent of matters in the 12 months ending June, while firms with 750 or more lawyers did so in only 3 percent of their matters.

The main reason the work is shifting to mid-size firms rather than small firms is because mid-size firms tend to be what lawyers call “full-service” — they have lawyers who can handle a variety of work, from intellectual property and employment law to litigation and regulatory work. Small boutique firms typically focus on only one or two types of law.

Kris Satkunas, the lead author of the report, said the trend will likely continue if in-house lawyers are satisfied with the quality of work mid-size firms are doing.

“Once a corporation is able to save significant money and get quality service at a lower price, it’d be hard to imagine they would then turn around and spend significantly more,” said Satkunas, director of strategic consulting at LexisNexis.

Other highlights from the report:

• The average U.S. law firm partner bills $381 an hour — 2.7 percent more than a year ago.

• The highest-paid partners work on mergers and acquisitions and earn $630 an hour, followed by general corporate law ($575 an hour), trademark ($527 an hour), regulatory ($513 an hour) and patent ($500 an hour).

• Hourly rates among Washington area law firm partners are rising 1 to 2 percent a year — that’s less dramatically than in than New York, Los Angeles and San Francisco, where rates are rising 2.1 to 3 percent.