With so much foreign money pouring into U.S. property markets over the past few years—inflating prices and cutting returns—American investors increasingly are looking offshore for higher yields. There’s just one catch: The spread between U.S. and offshore returns is narrowing. Demand is strong globally, pushing down cap rates, and the ability to move money and market information at the speed of the Internet have left few undiscovered pockets of above-market opportunity.

Still, there is clearly more U.S. money looking for returns abroad. A recent survey by institutional real estate newsletter Real Estate Alert found that a total of 21 domestic operators are overseeing 26 funds that invest solely outside of the U.S. Tishman Speyer Properties, for example, is raising $1.3 billion for a series of funds that will target India, China and Europe. It’s also planning to launch a Brazilian joint venture.

Maybe in the remote Amazon, Tishman will find bargains. But, elsewhere they are hard to come by, says Jim Costello, senior economist at Boston-based Torto-Wheaton Research. “Yields seem to be bid down to similar low levels across the U.S. and the world,” he says. Costello notes that rising land prices in Japan, strong economic growth in Eastern Europe and heated demand for properties in the largest Chinese cities have flattened yields in those markets. As a result, he says the best places to look for opportunity now may be in such capital-starved markets as Ukraine and in the Baltic states. Office yields in these markets hover near 8%, according to Jones Lang LaSalle.

Even now, it’s too late to get 8% in Poland. Until recently, the yield on a stabilized Polish office property was easily in the double-digits, but buyers from Western Europe have pushed east, forcing yields on Polish office properties down into 7% territory—well below an emerging market yield.

John Falco, principal at San Francisco-based real estate consulting firm Kingsley & Associates, says that while yields have fallen overseas, risks have not disappeared. These include political risk, partner risk and currency fluctuations which today’s returns may not justify. Even conservative institutional investors are chasing yield overseas, Falco notes: “I remember 10 years ago talking to some of the largest pension funds about foreign real estate investments. Back then, none of them had any international exposure. Now many of them are taking a portion of their 5% allocation and investing in these offshore funds.”