(FORTUNE Magazine) – The quest for income in today's low-yield economy is beginning to resemble the search for intelligent life in the universe: Believers know it's out there but aren't sure where. Meanwhile, back on earth, three-month CDs throw off just 2.7%, annualized, and even 30-year Treasuries now cough up a mere 6.7%. Of course, bond and other mutual funds give you a shot at higher income and offer ! diversification too. But what kind of fund should you buy, given the oodles to choose from? Ginnie Mae or junk? Corporate or convertible? Mortgage-backed or muni? Enter the so-called flexible-income fund. This ilk invests in a wide variety of bonds, convertibles, or stocks, typically shifting among them to find maximum income and, often, hefty capital appreciation to boot. According to Lipper Analytical Services, flexibles as a group yielded 6.7% and toted up an impressive total return of 11.9% in the 12 months ended May 31. As investments, that puts them somewhere between junk bonds, which had a 16% total return over the same period, and short-term U.S. Treasury funds, with 6.5% (see table for how some top-performing flexibles did over five years). Choosing a flexible fund may require more homework than selecting a plain- vanilla corporate bond fund, because the flexibles' investment strategies vary greatly. Some tilt sharply toward particular asset classes, like high- rated corporate bonds, for example. Others might prohibit investment in junk bonds or limit exposure to equities. Advises Jack Ryan, a co-manager at Vanguard Wellesley Income: ''More so than with other funds, people should try and understand how flexible-income ones achieve their returns before they invest.'' Most prospectuses spell out the emphasis the funds place on income or capital appreciation, and how risky the managers think their investment strategy is. As with other investments, higher yields often signal bigger risks. So decide how much danger you can tolerate. Also, look at how consistently the fund has met its income objectives in the past. Pay close attention to loads and fees; while yesterday's double-digit returns covered high expenses, today's low yields could mean a proportionately bigger bite out of investor returns. If safety is your prime concern, few flexible funds can beat the First Prairie Diversified Asset fund. One reason: It won't invest in junk or unrated bonds. Instead, fund manager Arthur P. Krill goes for better-rated bonds, spreading this part of his portfolio among different maturities to dampen sensitivity to rising interest rates. He tries to boost total return by finding undervalued convertible bonds and common stocks that will appreciate. Prairie has returned 13.2% annually over the past five years. At Wellesley Income, Ryan tries hard to keep the fund invested 35% to 40% in equities and the balance in bonds. If the value of the stock holdings falls, he buys more to bring the fund back to his ideal ratio. Says he: ''Think of it as a self-correcting mechanism that forces us to put money into the undervalued asset.'' It's worked, allowing him to chalk up returns of 13.9% annually over the past five years. While Wellesley won't sink money into junk, more than 20% of its fixed-income portfolio is in mortgage-backed securities. On the equity side, Ryan is focusing on lower-than-average-yielding utilities that are likely to raise dividends. MANY a mortgage-backed fund has taken a beating of late: As interest rates have fallen, homeowners have prepaid their mortgages, giving fund managers their money back at a time they didn't really want it. An exception: the USAA Income fund, which has a gigantic 56% of its assets in mortgage-backeds. Fund manager Jack Saunders bought many high-yielding mortgage-backeds at discount and took his profits as the bonds were paid off early, at par. He has also bought mortgage-backed securities with yields in the 7% range, which makes them less vulnerable to prepayments. Other flexible funds with solid returns are Seligman Income, where manager Charles Smith cuts risk by keeping 42% of his portfolio in the conservative areas of the convertible-bond market, and Advantage Income, whose Susanne Stauffer balances an 8% exposure to junk bonds with higher-rated bonds that have an average ten-year maturity. Such bonds, she says, provide the best combination of total return and low volatility. Want something flashier? The Berwyn Income fund, run by the father-and-son team of Robert E. and Robert P. Killen, has been investing upwards of 30% of its assets in junk bonds -- and making a killing. Over the past 12 months the fund has returned 17.5%.

CHART: NOT AVAILABLE CREDIT: ALAN BASEDEN FOR FORTUNE/SOURCE: LIPPER ANAYLTICAL SERVICES: FUND PROSPECTUSES CAPTION: SIX WAYS TO FLEX