One of the authors of a key piece of NSA reform sympathized with certain critics of the legislation on Tuesday, and admitted that the bill doesn’t address key areas of surveillance abuse.

Rep. Jerrold Nadler (D-N.Y.) pledged, however, that that reformers would try to fix some of the bill’s shortcomings next month using the power of the purse.

“There’s some criticisms of the USA Freedom Act that it doesn’t go far enough—criticisms that’s I’d agree with,” Rep. Nadler (D-N.Y.) said Tuesday morning, on CSPAN’s Washington Journal.

“But we’ll get another chance,” he noted, referring to ”appropriations bills coming up next month.”

One of the security state’s authorities that Nadler singled out as in need of revisions not provided by the USA Freedom Act was Section 702 of the Foreign Intelligence Surveillance Act. Former NSA contractor Edward Snowden revealed that the law permitted the agency to scoop up internet communications of foreign individuals—a task that inevitably results in the collection of sensitive information about Americans’ social networks, as well.

“We ought to rein that in somewhat and control it,” he said.

The annual Department of Defense spending bill will be marked up in a closed Appropriations subcommittee session on Wednesday. It will then move, along with other appropriations bills, to the House floor for a full vote, most likely in June—after the current kerfuffle over the USA Freedom Act and expiring PATRIOT Act provisions has been settled (assuming that there is neither a short-term reauthorization nor total inaction).

In previous years, NSA reformers have used the defense spending bill as a means to codify new restrictions on the NSA.

An effort by Reps. Justin Amash (R-Mich.) and James Conyers (D-Mich.) in 2013 to cut funding to the agency’s telephone metadata collection program was defeated by a slim margin.

The following year, reformers in the House succeeded in advancing an amendment to the defense spending bill that would have barred the NSA from searching its foreign intelligence surveillance databases for communications involving to American citizens. The measure, sponsored by Reps. Zoe Lofgren (D-Calif.), Tom Massie (R-Ky.), Rush Holt (D-N.J.), and Ted Poe (R-Texas) passed the House overwhelmingly last June, but the policy rider was stripped out of the budget at the end of the year, during an annual fiscal legislative process known in 2014 as the “Cromnibus.”

Despite the criticism he leveled at his own legislation being insufficient, Nadler testified before the House Rules Committee the night before the USA Freedom Act was passed by the House 338-88, and advocated for the important parliamentary panel to bar the full vote from considering amendments.

“Make sure that the carefully negotiated agreement that has broad support on both sides of this house is maintained,” Rep. Nadler told the Committee.

Just how far reformers may go to exploit the appropriations process to tie up the NSA will depend on what the Senate does with the House-passed bill. .

Senate Majority Leader Mitch McConnell (R-Ky.) placed the legislation on the Senate calendar this week, meaning the upper chamber could vote on it before Congress’ Memorial Day recess. The break runs past the June 1 expiration date for PATRIOT Act surveillance authorities.

McConnell has also scheduled a “clean” PATRIOT Act reauthorization vote, despite vows to attempt to filibuster any such move by Sens. Ron Wyden (D-Ore.) and Rand Paul (R-Ky.).