TREASURIES-Yields climb after strong U.S. 3-year note auction

* U.S. 3-year auction shows strong demand

* Focus on $23 billion, 10-year auction (Updates prices, adds comment, auction results)

NEW YORK, Aug 8 (Reuters) - U.S. Treasury yields rose on Tuesday, bolstered by strong demand for three-year notes in an overall quiet market as investors awaited the sale of more debt securities this week and the expected reduction of the Federal Reserve's balance sheet next month.

Trading volume has been half its normal average, analysts said, as the market gets into the thick of the summer months, with activity in Japan, whose central bank is the largest non-U.S. holder of Treasuries, shut down next week for holidays.

Tuesday's U.S. three-year note auction had a strong showing, with a high yield of 1.520 percent, compared with market expectations of 1.530 percent at the bid deadline.

Bids totaled $75.1 billion for a 3.13 bid-to-cover ratio, up from last month's 2.87. The 3.13 cover was the highest since October 2015. Indirect bidders, consisting of foreign central banks, took a robust 64.1 percent, higher than the 52.6 percent demand from July's auction.

"We expected a strong reception and that's basically what we got, though we did have some concerns given the U.S. Treasury rally just ahead of the auction," said Aaron Kohli, fixed income strategy director at BMO Capital Markets in New York.

Investors are now looking to Wednesday's auction of $23 billion in U.S. 10-year notes.

Societe Generale in a research note said the current 10-year note yield is expensive on an outright basis, and needs to sell off more in order to entice buyers.

Another negative is the fact that 10-year yields came in above the expected levels in five of the last six auctions, the French bank added.

In late trading, U.S. 10-year yields rose to 2.274 percent , from 2.257 percent late on Monday.

U.S. 30-year bonds yielded 2.858 percent, up from 2.837 percent the previous day. Yields earlier hit a one-week high.

After the auction, U.S. three-year yields were at 1.510 percent, up from Monday's 1.505 percent.

The U.S. yield curve continued to steepen for a third straight session on Tuesday, with the spread between the five-year and 30-year rising to 103 basis points.

Overall, a steeper yield curve suggests investors may finally be pricing in some inflation, especially after last week's U.S. nonfarm payrolls report showed a rise in wage growth in July.

Investors are bracing for key events such as the start of the unwinding of the Fed's balance sheet in September after a prolonged period of quantitative easing. Some analysts said the impending balance sheet reduction has diminished the need to raise interest rates again this year. (Reporting by Gertrude Chavez-Dreyfuss; Editing by Paul Simao and Lisa Shumaker)