With the economy stumbling, finance professionals seeking new jobs and new challenges are finding themselves in a market that rather suddenly has grown more competitive.

Because of the Bear Stearns meltdown and fears that other financial services firms might cut back on staff, a flood of job hunters has poured into the market in recent weeks. But they are fighting for fewer available positions, with some finance executives deciding that now is not the time to leave a stable post to take a chance on a new one.

“It’s become more of a buyer’s market,” says Lorraine Hack, a partner in the financial-officer practice at recruiter Heidrick & Struggles. “We’ve been getting tons more résumés and inquiries lately. People at the financial services firms see the potential writing on the wall and they want to be proactive.”

If you’re considering a career move for whatever reason, what should you do differently in the current economic environment and competitive job market? The key, according to Hack, is open-mindedness.

“To differentiate yourself, be open to different jobs and industries,” says Hack. “People feel they will appear unfocused if they don’t have a specific objective on their résumé and don’t target an industry — like, ‘I’m seeking a treasurer position in financial services.’ But I think it’s just the contrary. You pin yourself down that way. Finance is really the most transferable across industries of all the corporate skill sets, and a fresh perspective and mindset can be quite valuable.”

At the same time, though, it can be a fruitful strategy to take a special look at filling roles that thrive during hard economic times, such as restructuring and bankruptcy work. Also, some industries, as widely different as healthcare, consumer products, and liquor, are relatively recession-proof and could provide good options for those seeking stability. And many hedge funds are continuing to do well despite the overall economic malaise, notes Barry Bregman, financial services partner at executive search firm CTPartners.

A crucial step anytime one is looking for new work, but especially when the market is tighter than usual, is to do a “self-audit” — something to which finance executives should be able to relate. Take stock of everything from goals and contacts to networking lunches and thank-you notes.

Getting down to numbers, Annie Stevens, a managing partner at Clear Rock, an executive coaching firm, suggests that executives spend 70 percent of their job-hunting time networking, 15 to 20 percent working with recruiters and search firms, and the rest on direct mailing or cold calling. Less than 8 percent of new jobs are found from direct mailings or job postings, she said.

Many job seekers struggle with networking, finding it an awkward mix of pandering and socializing. But it is crucial, especially to provide a safety net for the possibility that the need for a job search will arise during a period of tight employment. “If you haven’t reached out to your network while you were happy and working, people will find it distasteful when you run to them and ask for help,” says Bill Behn, director of staffing for SolomonEdwardsGroup, a CFO services firm. “You need to have a give-and-take mentality.”

To cultivate a network of people who will help in lean times, Behn suggests doing people favors, sending helpful emails, and making a point of being in touch when you don’t need anything.

People who have been caught up in a downsizing often are embarrassed to pick up the phone and call former colleagues and clients, Bregman notes. “But you shouldn’t hesitate to follow up with people with whom you have a long history,” he says. “They generally will be very supportive. The reality is that they will understand that this is a downturn and that there are sectors and companies that are laying off, and that it has nothing to do with your performance.”

Another pitfall is denial. Bregman says he recently has spent “a lot of time on the phone with people from Bear Stearns. Some of them are just distraught, but others are thinking that they’re superstars and JPMorgan is going to keep them. But you’ve got to be realistic — JPMorgan is not going to keep that many people. A third approach is best, which is to be honest and open with yourself and the people you call.”

Getting hired in a slowing economy also requires more patience, especially in a high-paying field such as corporate finance. It is well known that the more money you earn, the longer it takes to find a new job, notes Behn.

Creativity can be the best means of “product differentiation” for an executive on the prowl. “Be persistent, thoughtful, and innovative,” says Eric Rehmann of Korn/Ferry International, another executive search firm.

Stevens of Clear Rock notes that creativity can mean tapping into the “hidden job market” with social networking websites such as LinkedIn, Facebook, and MySpace, rather than traditional Internet job boards. “Fewer job openings mean more people are chasing advertised and posted positions,” she says.