Carl Levin, a Democrat, represents Michigan in the Senate. Lamar Alexander, a Republican, represents Tennessee in the Senate.

The U.S. Senate — one-half of one branch of our government and an institution crucial to resolving serious issues before our country — is routinely described as dysfunctional, gridlocked and broken. We feel obligated to do something about it.

That’s why we went to the Senate floor last week to encourage our colleagues to embrace a classic virtue: self-restraint.

Senate rules require, at most steps of the legislative process, agreement from all 100 senators; absent unanimous agreement, they entail a time-consuming process that requires a supermajority of 60 senators to move forward. Such rules protect minority interests. The Senate’s constitutional function is to rein in the haste that can grip other institutions in our federal system. But if every senator exercises his or her rights at once, nothing happens.

One area in which the Senate has had a hard time reaching unanimous consent is how to deal with amendments. Frequently, senators in the majority think those in the minority introduce amendments to delay bills or raise extraneous issues. Those in the minority think the majority unduly restricts consideration of amendments. The result is often gridlock.

We propose an approach that should be useful on many pieces of legislation: If the minority members would allow the majority leader to bring a bill to the floor for a vote without the 60-vote process, the legislation would be open to all relevant amendments but not to nonrelevant amendments.

Last week’s action on postal reform shows how our approach works. The minority joined the majority in bringing to the floor legislation to resolve the U.S. Postal Service’s substantial problems. The majority leader asked for unanimous consent that all amendments to the bill be relevant. One senator objected because he wanted to offer an amendment on Egypt, a serious matter but one not related to a discussion of the Postal Service.

Under Senate rules, that senator had a right to raise that amendment. But the majority leader has rights as well, and he used them to block the irrelevant Egypt amendment. To do so, the majority leader had to control all amendments. What began as a promising week of debate on the dire straits of the Postal Service became three days of no progress while we sought to break the deadlock.

This was a waste of time. Fortunately, all senators finally agreed to consider only relevant amendments. In turn, the majority leader agreed to a lengthy list of relevant amendments offered by Republicans and Democrats alike.

This approach of self-restraint will, we hope, become a good example of how the Senate can operate. The only improvement would have been to have reached the agreement three days earlier.

Many senators would like to eliminate the requirement that the majority leader must go through the time-consuming 60-vote exercise to proceed to a bill. Others think that any senator should be able to offer, at any time, virtually any amendment and have it debated and voted upon. But resolving those issues would require a debate that is probably beyond the reach of the current Senate.

The approach that we advocated for the postal-reform bill could be used more often to deal with important legislation. In exchange for allowing a bill to come to the floor without the 60-vote exercise, every senator would agree to limit consideration of amendments to those relevant to the bill before us. Vigorous and extended debate on the substance of important bills would still take place. Senators would have ample opportunity to offer amendments. But our proposal would give senators a more effective way to deal with the issues voters expect us to consider and would help restore public confidence in the Senate.