SINGAPORE — Last year, American law enforcement officials pressed the Swiss bank UBS about Henry Hsiaw, a Taiwan-born American whom they accused of failing to file tax returns.

The world has changed since the days when Swiss banks stood as the peak of privacy for the rich. Already, UBS had paid $780 million in fines and disclosed details of thousands of Swiss bank accounts held by Americans — including the records of one account controlled by Mr. Hsiaw.

Still, UBS balked at handing over information about Mr. Hsiaw’s account with the bank in Singapore. That information, it said, was protected under the Asian city-state’s bank secrecy laws.

That courthouse dispute illustrates the growing pressures on Singapore, an increasingly popular destination for money that wants to stay under the radar. Tight bank secrecy laws have helped draw $1.1 trillion in foreign funds to the city, according to an estimate from Boston Consulting Group, a consulting firm. Singapore is now growing faster than Switzerland and is set to become the largest cross-border financial center in the world by 2028, the firm forecasts.