Should a second nuclear bomb been used in World War 2?

It was used because:

1. Truman's order authorizing use of the bomb authorized use of all bombs available as soon as they became available and conditions were suitable for delivery, until Japan surrendered.
2. The first 2 bombs became available about the same time.
3. Japan did not surrender until 5 days after the second bomb.
4. The third bomb became available 4 days after Japan surrendered and so was not used.

It would have taken a special order direct from Truman, canceling his previous authorization order to prevent the second bombing. Not very likely.