Senators on both sides of the aisle have demanded transparency lately from a growing list of government agencies: the State Department, the Justice Department, the IRS, the National Security Agency.

Yet when it comes to their own dealings, most notably their campaign fundraising and spending, senators don’t look so keen on transparency after all. Unlike virtually all other political players, senators file their campaign finance reports on paper instead of filing them electronically. This perpetuates a costly, cumbersome and increasingly ludicrous tradition that hampers full disclosure.

“As senators call for more transparency in other branches of government, we can start in our own backyard,” said Sen. Jon Tester, D-Mont., who is pushing for a fix. “The Senate’s campaign finance reporting is stuck in the dark ages, and it keeps Americans from quickly finding out who is funding candidates’ campaigns.”

Tester is author of a bill that would drag the Senate into the 21st century and that may finally get a full hearing in this Congress on the Senate floor. The Senate Campaign Disclosure Parity Act, which would require senators to file all election-related reports electronically with the Federal Election Commission, already has 34 co-sponsors, including five Republicans, and may soon tack on a few more.

One backer is Sen. Charles E. Schumer, D-N.Y., who chairs the Senate Rules and Administration Committee, where a similar Tester-authored bill won a favorable hearing in the previous Congress. Admittedly, Senate electronic filing legislation has been introduced in every Congress since 2004, only to be scuttled by secret holds and poison pills — often traceable back to Senate Minority Leader Mitch McConnell, R-Ky., a leading foe of political money restrictions.

But the Supreme Court’s 2010 ruling to deregulate political spending, which has aroused public concern over unrestricted — and often undisclosed — political money, has given Tester’s bill a boost. House members, presidential candidates, political action committees, political party committees and 527s have all filed electronically for more than a decade.

“It’s almost reasonable for some senators to believe that this is such a minor bill that it won’t generate much attention,” said Craig Holman, government affairs lobbyist with Public Citizen. “But it’s getting out into the public dialogue.” Public Citizen and 10 other government watchdog groups wrote senators last week to urge them to back Tester’s bill.

At a time when tech-savvy senators raise money online and publicize their lives on Facebook and Twitter, the notion that they would dump some 380,000 pages of paper records on the secretary of the Senate every quarter — often via the U.S. Postal Service — looks increasingly absurd.

The documents travel a circuitous route from the secretary of the Senate to the FEC, then to an outside contractor for data entry, and back again to the FEC for uploading. The whole process takes up to two months, so donations made in the final quarter of an election often cannot be searched until the race is over.

Not to mention the exorbitant cost: The Office of Management and Budget estimates that paper filing costs taxpayers $430,000 a year — no small sum when sequestration has forced painful cuts in areas from medical research to public parks. Both the secretary of the Senate and the FEC endorse the switch. Even President Barack Obama called for Senate electronic filing in his annual budget request this year.

“We have never found a senator, including McConnell, who publicly opposes this legislation as it stands,” said Lisa Rosenberg, government affairs consultant with the Sunlight Foundation. “No one does. We have the votes. It’s just procedurally challenging to get it to happen.”

Absent a legislative remedy, the Sunlight Foundation is urging senators to at least follow the lead of Tester and about a dozen of his Senate colleagues, who voluntarily submit their campaign finance reports electronically. Tester has gone one step further and posts his daily schedule online, including all meetings with lobbyists — something the Sunlight Foundation also promotes.

Tester said his bill “will save taxpayer money, and hold the Senate to the same level of accountability that folks around here are demanding from others.” He’s hopeful that the Rules Committee will take it up again soon, and that Senate Majority Leader Harry Reid of Nevada, another backer, will bring it to a vote by unanimous consent.

The question, of course, will be whether senators prove willing to act on the transparency principles they talk about so much these days. Noted Holman: “If we can get a vote, we’ll see whether there are enough senators who are embarrassed enough to do the right thing.”

Eliza Newlin Carney is a senior staff writer covering political money and election law for CQ Roll Call.