Private equity (PE) investors are cautiously returning to Asian markets, this time with greater savvy.

Capital began flowing into the region after the global financial crisis, but that was reversed in 2011 and 2012 because investors sought relatively cheap deals in the safer developed markets depressed by the crash.

Investors have been more reticent to invest in PE following the crisis. In a survey of 50 managers worldwide, Private Equity International found it had raised $586 billion between 2008 and 2013, about 17 percent less than in the five years to 2007. In 2007 alone, 18 mega funds raised $182 billion.

The total value of PE deals dropped 16 percent in 2012 from a year earlier, according to management consultancy Bain & Co.

PE investments are growing again, particularly in China, some parts of the Association of Southeast Asian Nations (ASEAN) and a few other Asian markets where opportunities again beckon.

A study by London-based research group Preqin of 100 institutional investors in June 2013 found that 50 percent thought Asia presents the best opportunities among all emerging markets.

But investors are now much more cautious and regulators less likely to spread the welcome mat without careful consideration.

"In 2013, European and American markets recovered, which is obvious. Capital was withdrawn (from Asia). The Asian market was less active in 2013," says Li Yao, CEO of the China-ASEAN Investment Cooperation Fund, a PE fund with investment from the Chinese government.

"Asian emerging markets' performance in 2013 was not as good as 2012," he says. "The market stepped into a fluctuation period in 2013."

But interest is definitely rising among investors.

Kohlberg Kravis Roberts & Co (KKR), one of the world's largest PE outfits, raised a record $6 billion to invest in Asia last year. It is the largest single pool of investments in the region. TPG, one of its competitors, also raised a fund that exceeded its $5 billion target. Carlyle Capital raised $3.5 billion. Bain Capital raised $2.3 billion in 2012.

Preqin said Asian funds managed to attract $30 billion in 2012.

However, the amounts earmarked for Asia remain a fraction of what goes to the United States. The US is the single largest market for PE groups, with 171 members in the PEI 300, Private Equity International's index of the largest PE firms. Asia and Europe have roughly the same number of funds in the ranking, with about 53 each.

Still, investors are again putting funds into Asia. But they are doing so with greater awareness of what can and cannot be done in the market and knowing that returns, once believed to be near mythical, are not easy to generate.

One example is the new KV Asia Capital fund, which raised $263 million as of last August to invest in medium-sized firms.

"KV Asia Capital has a 'bottoms-up' approach and we are seeing deals from across the Southeast Asian region, especially Singapore, Malaysia, Indonesia, Thailand and the Philippines," says Karam Butalia, the fund's executive chairman. "We do deals with the right mixture of quality, value and growth."

"Pan-Asian and global funds tend to be larger and hence target a larger deal size," says Butalia, who expects deals to ramp up through the year. "Our deal sizes and local cultural understanding results in our competing more with local Southeast Asian funds only."