Consumer prices fell by 0.1% in the month of July, but were up 0.7% in the year to that month.
Tobacco and alcohol were up by over 6% in the year followed by education costs, which were up almost 5%, according to the figures from the CSO.
There were price falls in furnishings and household fittings as well as clothing and footwear, both of which were down around 3% in the year.
The annual rate of inflation in the services sector was 1.4% in the 12 months to July.
When mortgage interest payments were excluded, that rate increased to 2.3%.
Goods inflation showed no change in the year.
In its note on the figures, Investec points out that the rate of inflation in the private rental sector increased to 7.2% in July, its fastest pace of growth since early 2008.
It says that the muted headline rate of inflation continues to provide some respite for consumers.
However, chief economist Philip O'Sullivan cautions that any further increases in indirect taxation in October’s budget could translate into upward pressure on prices in the short term.
Davy pointed out that falling mortgage interest rate costs are being offset by a renewed rise in energy prices.
"Energy prices rose 1.4% in the year to July, but this was more than offset by a 8.6% fall in mortgage interest costs - the impact of the May ECB rate now being felt," David McNamara of Davy said.
The group that represents small and medium sized businesses, ISME, expressed its concern at what it said was an increase in state controlled costs to business.
It said it believed these are the 'underlying efficiencies' that drive inflation and are disguised in the headline figure.
"The Government's main focus should be to create a business environment that allows companies the chance to grow. This can only be achieved through the reduction of our high cost base, starting with cuts to state controlled costs which have been continuously rising," Mark Fielding, CEO of ISME said.