ELITE management consultancies shun the spotlight. They hardly advertise: everyone who might hire them already knows their names. The Manhattan office that houses McKinsey & Company does not trumpet the fact in its lobby. At Bain & Company's recent partner meeting at a Maryland hotel, signs and name-tags carried a discreet logo, but no mention of Bain. The Boston Consulting Group (BCG), which announced growing revenues in a quiet press release in April, counts as the braggart of the bunch.

Consultants have a lot to smile about (see table). The leading three strategy consultancies have seen years of double-digit growth despite global economic gloom. In 2011, the last year for which Kennedy Information, a consulting-research group, has comparable revenue numbers, Bain grew by 17.3%, BCG by 14.5% and McKinsey by 12.4%. All three are opening new offices.

Big trends that befuddle clients mean big money for clever consultants. Barack Obama's gazillion-page health reform has boosted health-care consulting; firms would rather pay up than read the blasted thing. The Dodd-Frank financial reform has done the same for financial-sector work. Energy and technology are hot, too.

Companies are reluctant to talk about their use of consultants, and consultancies are relentlessly tight-lipped. Bain is said to use code-names for clients even in internal discussions. Such secrecy makes this a hard industry to analyse.

It also lets stereotypes flourish. McKinseyites are said to be "vainies" (who come and lecture clients on the McKinsey way). BCG people are "brainies" (who spout academic theory). And the "Bainies" have a reputation for throwing bodies at delivering quick bottom-line results for clients.

In fact, the big three all learn from each other. All three now use their alumni networks to gather intelligence and generate business-something McKinsey is famous for. All three stake some of their fees on the success of their projects, a practice once associated with Bain. And all three show off their big ideas to the wider public, as BCG's founder was once among the few to do.

Consulting is no licence to make easy money. Cynics sneer that clients spend millions on consultants only to give the boss an excuse to do what he planned to do anyway. But that would be implausibly wasteful in these days of tight budgets. Consultants today cannot just deliver a slideshow and pocket fat fees. Even the elite three now make most of their revenue from implementing ideas, from finding ways to improve clients' internal processes and from other tasks not traditionally considered "strategy consulting".

As the elite firms move down into implementation and operations, they are meeting big new rivals hoping to move up into the loftier realms of strategy. Over the weekend of May 4th-5th partners at Roland Berger, a mid-tier consultancy, met to discuss a possible buyer for their firm. The most likely candidates are thought to be PwC, Deloitte and Ernst & Young, three of the "Big Four" accounting firms (the other is KPMG).

The big accountancy firms now do more consulting than McKinsey, BCG and Bain. Much of this involves manpower-intensive tasks such as technology integration. But their strategy and operations practices are ambitious, too. In January Deloitte bought Monitor, a brainy strategy firm, out of bankruptcy. In 2011 PwC bought PTRM, a respected operations consultancy. All four have scooped up smaller firms too. A successful Big Four bid for Roland Berger would reopen an old question: can the Big Four crack the elite tier?

It is too early to know whether the brainboxes of Monitor will fit comfortably into the Deloitte juggernaut. When EDS, a computer-equipment and services provider, bought A.T. Kearney, a midsized strategy firm, cultures clashed calamitously. A.T. Kearney bought itself free in 2006.

Nonetheless, Mike Canning, the head of Deloitte's strategy consulting in America, says the Monitor integration is going smoothly, and that clients are showing new interest in Deloitte. Is Deloitte competing with McKinsey, Bain and BCG for work? "Day in, day out, on a regular basis," says Mr Canning. Dana McIlwain of PwC echoes that: "We are definitely competing today, and only more so in the future."

Bob Bechek, Bain's boss, puts it differently: competition with the Big Four is up "very slightly in the past few years, but I mean like a couple of percentage points". He salutes the Big Four: they do what they do well and profitably. But he argues that the heavy-lift, repeatable work at which they excel is a different kind of business. Strategy consultants concoct novel solutions to unique problems, which is hard.

Rich Lesser, BCG's boss, acknowledges the challenge from the Big Four, but is confident. Having new rivals is nothing new, he says. Tom Rodenhauser of Kennedy Information reckons that the Big Four "are cracking the C-suite, but they're not first on the speed-dial for strategy work".

The elite firms are keen not to seem complacent. While boasting about opening offices in Bogotá or Addis Ababa they acknowledge that emerging-world bosses are not blown away by flashy names. The consultants aim to win trust with quick projects that show bottom-line results, before looking to book longer engagements.

Clients in the rich world are changing, too. Fifteen years ago Indra Nooyi, then the head of strategy (now the boss) at PepsiCo, was a demanding client for consultants, having been one herself at BCG. She was a rarity at the time. No longer: the consultancies have seen many of their alumni go on to fill senior positions at big companies.

Some, such as McKinsey, make it easy for big firms to poach their people, by putting potential employers directly in touch with consultants who tick the right boxes for a vacancy. The idea is that this outplacement service makes McKinsey a more attractive place to work. It also keeps the talent churning, constantly refreshing the firm's intellectual capital.

Clients are increasingly demanding specific expertise, not just raw brainpower. McKinsey and BCG, in particular, are hiring more scientists, doctors and mid-career industry types, and reducing the proportion of new MBAs in their ranks.

Vainie: "Vidi, vici"

The firms spend big sums on "thought leadership": ie, papers, books and conferences. This is not all airy-fairy theory. McKinsey has invested heavily in proprietary data. Its boss, Dominic Barton, says: "With the push of a button we can identify the top 50 cities in the world where diapers will likely be sold over the next ten years." The firm invests $400m a year on "knowledge development", and Mr Barton touts its "university-like capabilities" to impart it to its consultants.

It is fashionable to complain that consultants "steal your watch and then tell you the time", as one book put it. But customers clearly value what the consultants offer. Otherwise, the elite three and the Big Four would not be growing so fast.

Things are harder for the next tier, however. Old firms such as A.T. Kearney and Booz & Company (which considered but abandoned the idea of a merger in 2010) are seen by some potential clients as too small to bestride the globe but too big to be nimble. They will watch Roland Berger's fate with interest.

^{Correction: In the original version of this article the table mistakenly claimed that Boston Consulting Group has 6,200 employees. It actually has around 9,000 employees of which about 6,200 are consultants. This was corrected on May 14th. Our apologies.}