The dollar, which has dropped 5 percent against the euro over the past month, has a lot further to fall, says Stephen Gallo, head of market analysis at Schneider Foreign Exchange.

He told Bloomberg TV that the German economy, which shrank 3.8 percent in the first quarter, has probably hit bottom. Economic indicators in both the United States and Europe have stabilized, he points out.

"The market is pretty much convinced that in terms of economic contraction, we're already through the worst."

And fundamentals aren't necessarily paramount for the currency market now anyway, Gallo says.

"They're more responding to risk appetite. The main move we've seen in currency markets in the last two weeks is the pullback in the dollar, which we've been forecasting since at least December," he explains.

"We think that the dollar thumping is just starting to get going."

On another topic, Gallo says Eastern Europe may muddle through its economic woes.

"These are industrial nations largely ... not financial nations and necessarily as capital dependent nations as the United States and the U.K.," he notes.

Other experts are bearish on the dollar, too. "The dollar is usually strong during a global recession because of deleveraging and investor repatriation," Thomas Harr, senior foreign exchange strategist for Standard Chartered Bank, told CNBC.

But ,as the global economy bottoms, "and I think that's what we're seeing now, then the dollar will start to fall," he says.