Indeed, helped by Greek woes, the dollar index rose almost 0.5 percent on Monday to 97.35. That took the index, which measures the dollar's value against a basket of other major currencies, within sight of a one-month high hit last week of 97.775.
But analysts said that sharp falls in the euro were unlikely, and that talk of a move to parity against the dollar, which seemed so dominant just a couple of months ago, was unlikely to resurface in a strong way.
And that's because of a string of disappointing U.S. economic data that was keeping U.S. rate hike talk at bay for now.
Data on Friday showed U.S. gross domestic product declined at a 0.7 percent annual rate in the first quarter of the year compared with an initial estimate of 0.2 percent growth. The University of Michigan's consumer sentiment for May, meanwhile, marked a fall and the May Chicago Purchasing Manager's Index dropped unexpectedly.
"It's fairly obvious that Greece concerns are creating a lot of volatility. But we have the nonfarm payrolls report on Friday and that is going to convolute the story," Jane Foley, senior currency strategist at Rabobank, told CNBC, referring to one of the most closely-watched U.S. economic indicators.
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"We've seen the dollar recover since the middle of May, but if payrolls are weak then obviously the story is complicated and could slow the downside in euro/dollar," she added.