If you thought the Federal Reserve's interest rate increases have been gradual, wait until you see what it has planned for its $4.5 trillion balance sheet.

The central bank looks likely to begin reducing its bond holdings at a glacial pace given how uncertain officials are about the impact on financial markets, monetary policy and the economy. The aim, according to New York Fed President William Dudley, is to ensure that the drawdown is "a very modest, minor event."

"We want this very much to run in the background," he said at the Bombay Stock Exchange in Mumbai on May 11. So "we're going to do this in a very careful way that's very much well-communicated to markets."