The data pushed the euro, which is down as much as 6 cents against the dollar since early May, almost 0.2 percent lower in morning trade in Europe to around $1.34.
As yet, that did not look like the tiebreaker markets have been waiting for on the dollar's strength.
Speculation that the greenback could be beginning a longer-term push higher have grown after its best performance in a year and a half in July.
But a slightly softer than expected U.S. jobs number at the end of last week allowed some to take profits on that progress, leaving the dollar stuck just below a 10-1/2 month peak against a basket of currencies.
Sweden has been symbolic of Europe's flirtation with very low inflation, or even falling prices, this year, but its services PMI for July shocked by surging to 60.1 points from 54.6 a month earlier. That took the crown a third of a percent higher to 9.20 crowns per euro.
Sterling has also suffered in the past week, falling almost 1 percent against the greenback, but Britain's economic outlook is more positive than that for the euro zone.
The purchasing managers' index (PMI) for the services industry, which makes up around 78 percent of the British economy and employs about 80 percent of its workforce, rose to an eight-month high of 59.1, beating a forecast for 57.9.
Sterling hit a day's high near $1.69 after the data. It was last trading up 0.15 percent on the day.