* U.S. headline, core CPI rises in December

* U.S. jobless claims fall in latest week

* Investors slightly reduce amount of easing for 2024

* U.S. yield curve narrows inversion again

* U.S 30-year bond auction shows mixed results

* Fed officials strike slightly hawkish tone in comments

NEW YORK, Jan 11 (Reuters) -

U.S. Treasury yields slid on Thursday in volatile trading, led by falls on the short end of the curve, as hotter-than-expected consumer inflation for December did little to temper expectations about an early rate cut by the Federal Reserve.

U.S. yields hit session highs following the consumer price index (CPI) data, but have since meandered between gains and losses. The benchmark 10-year yield was last down 4.9 basis points (bps) at 3.980%.

"We're past peak market sensitivity to the inflation print, as we saw today. The Fed wants to do something," said Olumide Owolabi, head of U.S. rates, at Neuberger Berman.

"The key now is the timing of it, although we're not actually focused too much on that. We expect rates to bounce around within a tight range as investors debate the timing of the Fed easing."

U.S. data showed that the headline CPI rose 3.4% in December on a yearly basis versus the consensus forecast of a 3.2% increase. On a monthly basis, CPI advanced 0.3% versus expectations of a 0.2% gain.

Core CPI, excluding food and energy, rose 3.9% year-on-year, compared with forecasts for a 3.8% increase.

Following the inflation figures, U.S. rate futures have priced in a 71% chance of a rate cut in March, up from 68% late Wednesday, according to LSEG's rate probability app. But for 2024, there was less conviction for five cuts. Traders are betting on between four and five rate decreases of 25 bps each this year, putting the year-end fed funds rate at 3.8%.

"Although the core annual rate fell...the increase in the headline rate...will not convince the Fed that inflationary pressures are definitively slowing," said Stuart Cole, chief economist at Equiti Capital in London.

Investors will next look at U.S. producer prices data due out on Friday, a report that will be scrutinized to see whether the decline in oil has had an impact.

In a separate report on Thursday, initial claims for state unemployment benefits fell 1,000 to a seasonally-adjusted 202,000 for the week ended Jan. 6, data showed. Economists had forecast 210,000 claims for the latest week.

Jobless claims remain in the lower end of the 194,000-265,000 range that prevailed in 2023.

Also on Thursday, the U.S. Treasury sold $21 billion in 30-year bonds with mixed results. The offering priced well, picking up a high yield of 4.229%, lower than the expected rate at the bid deadline, suggesting investors did not really demand a premium to absorb the bond.

The bid-to-cover ratio, a measure of demand, was 2.37, with bids of $49.7 billion. The cover ratio was lower than last month's 2.43, but higher than November's 2.24. Indirect bidders, which include foreign central banks took down 67.8% of supply, compared with 68.5% last month..

Post-auction, U.S. 30-year yields were down 1.4 bps at 4.187%.

On the shorter end of the curve, U.S. two-year yields dropped 11.1 bps to 4.259%, on track for its largest daily fall since mid-December.

A widely-watched U.S. yield curve metric, showing the spread in yields between two- and 10-year notes steepened or reduced its inversion to minus 28.5 bps on Thursday. An inverted yield curve typically predicts an incoming recession.

Analysts called the yield curve move a bull steepener, in which short-term interest rate posted sharper falls than longer-dated ones. This reflects expectations the Fed will soon start cutting rates.

Fed officials who spoke on Thursday, however, leaned on the hawkish side following the CPI report.

Cleveland Fed President Loretta Mester said in an interview with Bloomberg TV said the U.S. central bank

needs more evidence

before cutting rates, noting a March move would be too soon.

In separate comments, Richmond Fed President Thomas Barkin cited the progress the Fed has seen in inflation this year, with some measures close to the 2% target over the past six months, "you'd have even more reassurance...

if it were broader based

" and included a slower pace of price increases for services and housing costs. (Reporting by Gertrude Chavez-Dreyfuss; Additional reporting by Siddarth S. in Bengalaru; Editing by Andrew Cawthorne, Nick Zieminski and Diane Craft)