SYDNEY, July 13 (Reuters) - The Australian and New Zealand dollars firmed slightly against a weaker U.S. dollar on Tuesday ahead of U.S. inflation data, but pandemic lock-downs kept pressure on the Aussie dollar.

The Australian dollar was 0.16% higher at $0.7490 but was still a long way from the month's top of $0.7599, as markets await the inflation data due at 1230 GMT. It has support at $0.7430 and faces resistance at $0.7520.

The kiwi dollar was also slightly higher at $0.6990 and further away from July's peak of $0.7104 hit early last week. Support lies at $0.6950 and the recent trough of $0.6923.

"The worsening Covid-19 outbreaks in Sydney is keeping Australian dollar under pressure," Commonwealth Bank of Australia strategists said in a note.

"Despite the recent pick-up in pace, Australia's vaccination rate remains low. The risk is the current Sydney lockdown is extended and/or tightened and drags on the Australian economy."

Markets ignored a measure of Australian business conditions that showed falls from record highs in June as coronavirus lockdowns curbed sales and undermined confidence, though activity was still solid by historical terms.

Australian bonds were little changed, with the yields on the 10-year Australian government benchmark one basis point higher to 1.337%, and the three-year bond yield half a basis point lower.

Across the Tasman sea, traders are expecting New Zealand's central bank to leave its official cash rate at 0.25% on Wednesday.

However, markets are already pricing in a hike in November and 75 basis points of cumulative hikes by late 2022, the most aggressive pricing across G10 central banks, according to JPMorgan economists.

New Zealand bonds yields were slightly lower across the curve, ahead of a busy few days of economic indicators, with second quarter consumer price data due on Friday expected to show a slight deceleration from the 0.8% increase in the previous quarter. (Editing by Kim Coghill)