A bipartisan Senate duo is again trying to permanently ban earmarks, a practice now out of favor with most members of Congress.

Patrick J. Toomey, R-Pa., and Claire McCaskill, D-Mo., said they will re-introduce a measure that fell short in the past session of Congress to write current party rules into law. They would define an earmark as “any congressionally directed spending item, limited tax benefit, or limited tariff benefit.”

Their bill would permit a budget point of order to be raised against any earmark and require a two-thirds majority vote to waive it, the lawmakers said in a statement.

Lawmakers have in the past few years honored what are effectively informal bans on directing spending to their favored causes and projects, reflecting decisions first made among GOP lawmakers to which Democrats have agreed. In February 2012, 38 senators joined McCaskill and Toomey in backing an amendment that contained pretty much the same proposal for banning earmarks.

The two senators are hoping to win over more converts this session, a goal perhaps made easier by recent abstention from the practice. Still, they seem unlikely to get the needed majority in their own chamber to advance their bill.

The existing bans have been effective, as fiscal 2011 and 2012 appropriations bills were completed without earmarks, and Congress seems unlikely to revive the practice anytime soon. House Speaker John A. Boehner, R-Ohio, is a longtime critic of the practice, and President Barack Obama has said he won’t sign any law that contains earmarks.

James P. Moran, D-Va., a veteran House appropriator, made what seems an ill-fated bid Wednesday to seek a potential revival of the practice. At the House Appropriations Committee’s organizational meeting, he asked another one-time defender of earmarks, Appropriations Chairman Harold Rogers, R-Ky., to consider creating a panel to look at whether they could be revived. Rogers didn’t respond at all to the request, and moved onto other committee business.