Spanish consumer prices fell again for their 11th straight month in May, by 0.2% year-on-year.
However strip out food and oil prices and core inflation rose year-on-year by 0.5%.
Price falls now appear to be near to working their way out of the system, the slackening rate in line with forecasts.
Spain began to emerge from a five-year recession in 2013, and this year growth is forecast to outstrip the EU average at over 3%. However the return of activity has yet to make much of a dent on unemployment, which still stands at nearly 24%, and double that for the youngest jobseekers.