CPI was 3.4%, down from 3.7% in April.
RPI was 5.1%, down from 5.4% in April.
Good news? Well, CPI is still one and half times over target, and the 2% target itself is rather generous.
Oh, and house price inflation has reached double figures again, not totally unexpected with the base rate at 0.5% - a historic low without precedent. Houses aren't in the CPI "basket" of goods so don't affect the index.
The fall in food prices is actually quite noticeable in the stops. There seem to be no end of special offers on at the moment.
Petrol hasn't fallen, but over the last few weeks there has been a pause in the relentless rise in the cost of a litre. Long may it last.