House Speaker Paul Ryan on Tuesday really, truly, officially and for good took his name out of running for the Republican nomination for president — “period, end of story.”

But he didn’t go quite so far as to say the delegates at the Republican National Convention in Cleveland could not consider someone else if they do not reach consensus on one of the three active candidates, although he indicated that a rule limiting nominations to candidates who ran for the presidency may be worthwhile. A statement that seemed to hint the Speaker would be open to considering dropped-out candidates like Wisconsin Gov. Scott Walker or Florida Sen. Marco Rubio.

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“I’ll leave it up to the delegates who that are looking to decide that,” he said. “I just really honestly believe if you want to be president, you should run for president.”

The Wisconsin lawmaker repeatedly has disavowed interest in the job for himself, but that has not stopped Establishment figures from floating the idea of installing him as the party’s standard-bearer at a contested convention. One British bookie recently even listed the odds of Ryan being the nominee at 1 in 9.

And it has not stopped speculation from skeptics that Ryan was leaving the door open. At a news conference at the headquarters of the Republican National Committee in Washington, he attempted to slam it shut once and for all, echoing the famous words of William Tecumseh Sherman.

“I want to put this to rest once and for all … We have too much to do in the House to allow this speculation to swirl, or to have my motivations questioned,” he said. “So let me be clear. I do not want, nor will I accept the nomination for our party.”

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And if that was not explicit enough, he spoke directly to the delegates: “If no candidate has a majority on the first ballot, I believe you should only choose from a person who has actually participated in the primary. Count me out.”

Ryan has a busy schedule as speaker, including the demands of crafting the federal budget. In addition, he faces a primary challenge in his House district from a businessman who contends that Ryan betrayed his constituents by supporting a budget last year that caved into President Obama’s demands.

Told by a reporter that he also had rejected the idea of becoming speaker before accepting the position, he said, “Those are apples and oranges. Being speaker of of the House is a far cry from being president.”