Alright, another idea: What if the A-Bomb is not used in WWII?
In my mind, there are two POD's to be used: say the USS Indianapolis, carrying parts for "Little Boy" is sunk a day before arriving at Tinian? The loss of these parts (including the enriched uranium) would mean that the bomb could not be constructed, and therefore would not be dropped. "Fat Man", the other bomb, could still be dropped, or else the US decides to hold on to it, unsure if it will work or not.
Second: By the end of June 1945, the Japanese were prepared to end the war. Reports to Emperor Hirohito that they were using the iron from bomb casings to make shovels. This basically means that the army is in no condition to fight a war anymore, much less win. So, he orders the reluctant cabinet to find anyway to end the war. The army officials went to the Soviet Union to see if they would mediate, but they wouldn't because they were preparing to attack Japanese holdings in Manchuria. So, what if instead they approach Spain, Sweden or Turkey, a neutral power, and tell them they are interested in peace. If they do so, then they will outline their requests in English (because possibly bad translation could have been a factor for America's rejection of peace terms earlier). Basically, they would agree to unconditional surrender, except that the Emperor not be forced to leave the throne.
So, say word of this gets to the US just as they find out they lost parts to the first atomic bomb? Perhaps Harry Truman and his advisers decide to look into this. Might be a possible coup in Japan when word leaks out, but I'm sure a message from the Emperor would quash any attempt at insurrection by the rank and file of the military.
So, we get pretty much the same results, maybe a month earlier, and without the need to drop a bomb. The Soviet Union will feel cheated out of a victory against Japan in Manchuria (increasing tensions between the fracturing alliance), and perhaps a colder Cold War?
What does everyone think?