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They adopted measures encouraging post offices to share space with local businesses, requiring regulators to consider the effect on the local economy before shuttering a post office and delaying rural closings for one year.

But they rejected an amendment offered by Mr. Coburn requiring workers to resign when they reach retirement age, which he said would help reduce the Postal Service’s bloated workforce. An attempt by Sen. John McCain, Arizona Republican, to establish a separate commission to preside over the changes went up in smoke.

Mr. Lieberman said the McCain amendment was unnecessary because the law already lays out a framework for reform.

“In this bill, we have constructed what I think is a clear and fair system of making exactly those decisions,” he said. “If this bill is enacted, there are post offices that will be closed — that simply has to happen — but it will happen according to a system of due process that gives more heed to the fiscal crisis of the Postal Service.”

Senators expect to finish working on the bill Wednesday.

In a late vote Tuesday, they turned back, by a 64-35 vote, an effort by Sen. Rand Paul, Kentucky Republican, to end the Postal Service’s monopoly on mailboxes. Under current law, only a letter carrier can place items in the mailbox.

Mr. Paul said a child putting a birthday invitation in a neighbor’s mailbox could net a $5,000 fine.

But Ms. Collins said ending the mailbox monopoly would open the post office to competition in urban areas while raising costs for delivery in rural areas.

“Continuation of the mailbox monopoly,” she said, “is necessary to preserve the safety, the security, the privacy of mail.”