Senate Appropriations Committee ranking Republican Thad Cochran (Miss.) announced Wednesday that he is supporting former Massachusetts Gov. Mitt Romney in the GOP primary, making him the first backer of former Sen. Fred Thompson (Tenn.) to endorse another candidate.

Romney hopes that Thompson supporters will vote for him in Florida next week. Winning the support of a veteran Southern senator like Cochran might help him reach that goal.

“I think Gov. Romney has laid out some ideas that will be received very well by the Congress: reducing taxes, letting people who are earning money from savings accounts, who are middle-class investors, be able to derive those benefits tax-free,” Cochran said. “This will encourage more saving; it will help strengthen our economy.”

The senator said Romney would bring to the White House the ability to work across party lines and “the same quality of leadership that he brought to the state of Massachusetts.”

Cochran also praised Romney’s “strong moral character,” adding that he was “impressed” with the former governor even though he had initially decided to back Thompson.

But not all of Thompson’s supporters are looking for new candidates to endorse.

Rep. David Davis (R-Tenn.) on Wednesday told The Hill that he does not plan to back another candidate and hopes Thompson will refrain from doing so, too.

The lawmaker said he is “still looking for a candidate who supports limited government and good strong Republican values.” In a reference to Thompson’s close relationship to Sen. John McCain (Ariz.), Davis said he knows there are “some friendships,” but he added that he hopes Thompson “doesn’t endorse either.”