* 30-year auction seen as weak
* Other Treasuries mostly up
* Jobless data causes no ripples
(Adds long-bond decline, late prices and comments)
NEW YORK, May 8 (Reuters) - Thirty-year Treasuries sat out a modest U.S. bond market rally and dropped on Thursday after the government sold $16 billion of new long bonds at unexpectedly high yields.
The 30-year auction, the last of three this week by the Treasury Department selling $69 billion of new debt, came with a high yield of 3.440 percent, or over two basis points more than the market level signaled just before the auction.
Viewed as a possible bellwether by many traders, the auction had a bid-to-cover ratio of 2.09, the lowest since an August 2011 auction and below a recent 2.36 average. Its high yield was the lowest since last June.
"The auction was weak," said strategist Ian Lyngen at CRT Capital in Stamford, Connecticut.
Yields on U.S. 30-year bonds, which on Friday touched their weakest level since June 19 at 3.34 percent, traded at 3.4123 percent after touching a high of 3.438 percent. For the day, the 30-year was down 4/32 in price.
Other Treasuries were mostly up or flat in price. Ten-year Treasury notes yielded 2.6035 percent, reflecting a price gain of 5/32.
"We have proven that it is possible for the 30-year to be too rich," said Jim Vogel, interest rate strategist at FTN Financial in Memphis.
Thirty-year Treasuries have risen sharply this year, in part on reported buying by pension funds that seemed indifferent to price increases.
But, according to Nomura analysts George Goncalves and Stanley Sun, some of the usual long-bond buyers did not show up.
"Non-dealers demand dropped to 48.8 percent, the lowest since June 2013 and much lower than the six auction average of 57.6 percent," they said in a commentary. "Investors finally shied away from the long end, given over-stretched valuations."
Traders also closely watched congressional testimony on Thursday by Federal Reserve Chair Janet Yellen, who on Wednesday reaffirmed had her dovish policymaking stance in another congressional appearance.
On Thursday, Yellen said the Fed is in no rush to decide the appropriate size of its balance sheet, but if it ultimately shrinks it to a pre-crisis size, the process could take the better part of a decade.
Early in the New York trading day, the government reported that the number of Americans filing fresh unemployment claims had declined 26,000 to 319,000. The data for the week through April 26 broke a three-week string of increases and was below forecasts.
Overall, the report suggested improvements in America's labor markets of a type that would usually weigh on bond prices.
(Reporting By Michael Connor in New York; Editing by Nick Zieminski)