DBWI: US used nuclear weapons against Japan

Truman decided against using the nukes against Japan, resulting in the massive and bloody invasion of the Japanese main islands. But what if the US had used nuclear bombs against Japan in mid-late 1945? Would that have sped the war up any?
 
In a way it would have. Keep in mind that the Japanese persisted despite a US invasion in the south, a Soviet invasion in the north, their cities being bombed to rubble, a mass famine, and the death of 5-6 million Japanese. In the end they only surrendered once it became clear they couldn't hope to repel the Allies (as Tojo put it "Our army was starved and fighting with weapons that became obsolete when the Portuguese came. Continuing further would only mean national suicide"). Given that I don't think the atomic bomb would lead to Japanese surrender, but the US would be able to destroy a number of Japanese cities and perhaps only would have had to launch Operation Olympic.
 
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