However, I wouldn't have wanted to make that decison -- Truman had to decide to to it or not to do it and sending the Russians a message was also important to him.
At the time of the A-bombing the only message Truman wanted to send to the Soviets was "Hurry up and declare war on Japan already!"
Then, we will really never know if the second bomb was unnecessary -- that part of the history is still cloudy. Que sera, sera.
The balance of the evidence seems to show that neither bomb was necessary, but this was not apparent to us at the time we dropped the bombs.
As I remember, there wasn't enough uranium or plutonium to make that third bomb functional -- just the casing existed. If you can find information disputing that, go for it.
The plutonium was actually on its way out the door at Los Alamos on August 11 when we got word that the Japanese were beginning to break. It was planned for use around August 17-18. We delayed the shipment for three days in the hope that it was unnecessary, but it set out for the Pacific on August 14. It never left US soil before we heard that they had accepted our surrender terms.
We were going to produce three bombs a month thereafter, expanding in December to more than 7 a month with a higher yield (mostly 37kt, but some 49kt bombs would have been possible).
Section 8.1.5 here does a good job of explaining it.
Those killed at the two bombing sites were civilians, we would have lost a small percentage of soldiers in that week. Some are going to believe it was a fair trade, some not. I've always been conflicted on that point but I would not in retrospect condemn Truman for dropping the bombs.
The 20,000 soldiers killed while awaiting deployment were not civilians. And while the arms-production factories and military headquarters were not "alive" to be killed, they weren't exactly civilian either.