* Corn prices climb for second day after report on Brazil crop, soybeans also higher

* Wheat pares gains

NEW YORK, Sept 20 (Reuters) - Chicago futures firmed on Wednesday, extending their rebound from this week's near three-year lows, rising on bargain-hunting, uncertainty about U.S. yields and expectations that Brazil could see a smaller corn harvest in the coming year.

The most-active Chicago Board of Trade (CBOT) corn contract was up 3-3/4 cents, or 0.8%, at $4.80 a bushel at 1808 GMT.

Brazil's food supply and statistics agency Conab late on Tuesday predicted a 9.1% drop in Brazil's total corn crop in the 2023/2024 cycle.

"That's a big drop," said Dan Basse, the president of Chicago-based AgResource Co. "As the U.S. market saw that, that was reason to cover shorts at three-year lows," he said. Commodity funds hold their largest net short position in CBOT corn futures since 2020, weekly data from the Commodity Futures Trading Commission shows, leaving the market prone to bouts of short-covering.

Soybean futures rose, bouncing a day after hitting their lowest levels since Aug. 16. The benchmark November contract was up 0.5% at $13.21-3/4 at 1808 GMT.

Traders continue to monitor yield reports from the early stages of the U.S. harvest to get a better fix on the size of the U.S. 2023 soy and corn crops.

On the export front, the U.S. Department of Agriculture confirmed private sales of 120,000 metric tons of U.S. soybeans to unknown destinations.

In a reminder of export competition from Brazil, the world's top soy producer and supplier, China's soybean imports from the South American country rose 45% in August from a year earlier, customs data showed.

CBOT wheat futures drew support from export demand from Egypt and Algeria, but profit-taking pared gains, traders said. CBOT December wheat was up 2-3/4 cents, or 0.5%, at $5.86-3/4 a bushel.

"We're finding some world demand. It's giving the wheat market a bounce here," Basse said.

In Egypt's tender, initial offers reported by traders showed Bulgarian wheat was offered cheapest before shipping costs, with Russian offers appearing to be aligned at a single price thought to represent the unofficial floor price.

(Reporting by Zachary Goelman in New York City. Additional reporting by Gus Trompiz in Paris, Naveen Thukral in Singapore and Peter Hobson in Canberra; Editing by Sharon Singleton)