The Flake Show is back, but in limited form.

Under the deal announced late Thursday in an epic floor discussion, House Democrats caved in to Republican demands that they disclose earmarks in future appropriations bills before they come to the floor in return for Republican leaders agreeing to limit the time and the number of amendments.

That means Rep. Jeff Flake (R-Ariz.), one of the few Members who regularly offer amendments to strike earmarks on the House floor, will have his chance to do so but will not be able to clog up the works with hundreds of amendments on individual earmarks.

The deal cleared the way for passage of the Homeland Security and military construction, Veterans Affairs and related agencies bills Friday, but will delay other bills by as many as three weeks so Appropriations staffers can vet the earmarks.

Republicans also won a promise by Democrats to change the House rules to create a point of order against conference reports that include “air-dropped” earmarks that were not in the original House or Senate bills.

Some Republicans, notably Rep. Dan Burton (Ind.), complained that such a vote would not allow Members to vote to strike individual earmarks. “We don’t really have a chance to cut out any of the pork,” Burton said of the Homeland Security and military construction bills.

But House Minority Leader John Boehner (R-Ohio) said it was not practical to do so on conference reports, because it could lead to a “pingpong” effect with the Senate.

The deal also includes a wrinkle on the Energy and water bill, which will come to the floor without earmarks. The bill will be held in the House until it can be combined with a list of earmarks that will be voted on and attached before it is sent to the Senate.

The deal, which requires unanimous consent and is thus tenuous, also requires appropriations bills to proceed under open rules.

Although Republicans declared victory in their battle against “slush funds for secret earmarks,” House Appropriations Chairman David Obey (D-Wis.) said the committee staff will have less time to vet earmarks and warned that more embarrassing ones might slip through.

The deal came after three days of obstruction from Republicans, which Obey said was tolerated because Democrats wanted to bend over backward to appeal to Republicans to vote for the bills.

Obey said he was “sorry” about proposing his plan not to include the earmarks in the first place, but reiterated that he felt it was a necessity given the tremendous workload his committee has had since the beginning of the year.