What’s the best way to boost your law firm’s brand in the United States? Go big.

That’s the takeaway from the second annual Acritas United States law firm brand index released February 26, which was compiled from a survey of 711 general counsel or equivalent at companies with revenue of at least $50 million.

Skadden, Arps, Slate, Meagher & Flom topped the list for the second straight year, followed by repeat runner-up Jones Day, Baker & McKenzie, in third place, and Latham & Watkins in fourth.

Acritas’s survey, conducted by phone between March and December 2012, asked respondents a series of questions about outside legal counsel: which five law firms first come to mind, which three firms do you favor most, which firms do you consider for bet-the-company litigation and major M&A transactions, and which five firms do you use for high-value work.

The survey also requested that foreign respondents name the law firms they use for inbound U.S. legal work. Firms received points for each question according to the order in which they were mentioned, with the first firm earning five points, the second getting four points and so on. About 10 to 15 percent of this year’s respondents replied to last year’s survey; the rest were first-time participants.

“Big is best when it comes to the U.S.,” says Lisa Hart Shepherd, chief executive officer and founder of Acritas, a market research and advisory firm. “It makes sense. When an organization starts to gain market share through mergers or organic growth they typically strengthen their brand.” Shepherd pointed to the index’s two biggest gainers as prime examples of this trend: McDermott Will & Emery, which surged from number 31 to 12th place and DLA Piper, which jumped six spots to number five. Both firms ranked among the top firms in The American Lawyer’s 2013 lateral report, with DLA adding 97 partners and McDermott hiring 42.

But those firms are not just growing, says Shepherd, they’re growing in the right places: overseas. “Every year in the U.S., 5 to 10 percent more of our respondents indicate that they have international needs, so each year those clients are having to look at those needs and say, ‘Who can help me now that we have a joint venture in China?’ ” Shepherd says. “Most people go with international firms as opposed to individual firms in individual regions.”

Both DLA and McDermott expanded worldwide in the past few years, with both opening offices in Seoul last year and McDermott also adding a Frankfurt location in 2012.

Jeff Stone, managing partner of McDermott, said the new offices the firm opened last year helped extend the firm’s brand, as did the attorneys it added in Shanghai and London. “Globally, we grew in important places and in important ways and that strategic growth has enhanced our brand,” Stone says.

But despite the emergence of mega-firms that have been born, in part, by the consolidation of the legal market, the U.S. market remains incredibly crowded, Shepherd says. “We generally see that the highest-ranking firm in a market captures around 40 to 50 percent of all awareness mentions, like Freshfields in the United Kingdom. In some of the other markets, a top firm might get as much as 70 percent,” says Shepherd. In the U.S. meanwhile, Skadden secured 17 percent. That means even as the big get bigger, in a saturated legal market, they’re fighting over smaller and smaller shares of brand awareness.