Headline inflation was much cooler than expected in June, and some economists say the Reserve Bank is now unlikely to lift interest rates next month.The annual rate of headline inflation is now 3.8 per cent, down from 4 per cent in May and 4.6 per cent in March.The slowdown in inflation has coincided with automotive fuel prices falling for three months in a row."Lower world oil prices as a result of some stabilisation in the Middle East in June contributed to fuel prices falling 10.9 per cent in the month," said Rachael McCririck, ABS head of price statistics."The federal government's fuel excise relief measures, which contributed to lower automotive fuel prices in April and May, also remained in place."With the chances of a rate hike next month appearing to shrink dramatically, it prompted an immediate sell-off of the Australian dollar on Wednesday.But economists say it is too early to assume that an economy-wide slowdown in inflation is in train.They say underlying inflation, which gives a more accurate picture of broader inflation pressures, remains uncomfortably high for the Reserve Bank.Underlying inflation was unchanged in June, sitting at an annual pace of 3.6 per cent, the same as in May."Although today's results were a little less than feared, they still won't provide a lot of comfort to the Reserve Bank," said David Bassanese, BetaShares chief economist."Despite a modest easing in the month of June, quarterly gains in the demand-sensitive areas of market services and housing remained uncomfortably higher over the quarter."Given a still somewhat tight labour market, ongoing energy cost risks and upward pressure on housing rents and new house prices, given recent tax changes, the risk of continued above-target inflation remains high."Goods inflation slowing, services inflation increasingThe Bureau of Statistics show that inflation in the price of goods has been slowing down in recent months, from an annual pace of 5.5 per cent in March to 3.5 per cent in June.But inflation in the price of services has been rising, from an annual pace of 3.6 per cent in March to 4 per cent in June.It is the same story with tradables and non-tradables.The "tradables" series measures the contribution of goods and services that are highly exposed to international trade influence (such as automotive fuel and most food items).The "non-tradables" series measures the contribution of goods and services most influenced by domestic factors (such as housing and education).Callam Pickering, Asia-Pacific economist at Indeed, said the RBA wants the prices of non-tradables and services to come down."To be consistent with the RBA's inflation target of 2-3 per cent, non-tradables inflation cannot afford to be much higher than 3.5 per cent and services needs to be closer to 3 per cent. Neither measure is anywhere close to that right now," he said."Lower headline inflation might convince some that higher rates aren't required: that'd be a mistake."Underlying inflation is the real story. It continues to drift higher, isn't meaningfully impacted by temporary factors, and isn't showing any signs of moderation," he warned.What's next for interest rates?David Robertson, Bendigo Bank chief economist, said he thought it was "highly unlikely" that the RBA would lift rates next month.However, he said there were still too many risks in the global economy for the RBA to feel too comfortable about the state of the world."The volatile oil price and related uncertainty around supply chains means inflationary risks haven't receded," he said."Second-order impacts [on food and groceries, and on construction costs] remain problematic, but the RBA has got ahead of the curve with their three rate hikes earlier in the year so 'rates on hold with a tightening bias' is still our view," he said.Citi economists Josh Williamson and Faraz Syed said despite the decline in headline inflation in recent months, persistent underlying inflationary pressures could still compel the RBA to deliver one final rate hike in November.If that happened, it would see the cash rate target rise from 4.35 to 4.6 per cent.Economists broadly don't think the RBA will hike rates next month, but EY chief economist Cherelle Murphy said given that underlying inflation is still relatively high and remained in June, the RBA could lift rates next month."The Monetary Policy Board meeting on 10 and 11 August will be a close call, and much will rest on the refreshed Reserve Bank staff economic forecasts," she said."Despite the welcome decline in the rate of headline inflation, we expect the still-high level of core inflation and ongoing risks to narrowly tip the balance for the Monetary Policy Board to lift the cash rate to 4.6 per cent, the highest in 15 years," she said.But Westpac chief economist Luci Ellis said she no longer expects the RBA to hike rates this year."Inflation has been more benign than we feared and the RBA forecast," Ms Ellis said."The substantial pass-through of higher energy costs seen in the early phase of the Middle East conflict has not been followed up in recent months."Although we still expect the RBA Board will debate the case for a hike, things have not turned out in a way that supports the case for one."