Actually there was a third alternative--blockade. General Lemay and the Navy would have welcomed this alternative as a means of bolstering the value or their respective branches of service. Most of the casualty estimates provided to Truman including that by Douglas MacArthur predicted around 30k American deaths and around 100k wounded in the conquest of Japan. No one predicted hundreds of thousands of American deaths in the event of an invastion. That figure was raised after the war partly to justify the bombing in the face of revisionists. Kokura was the primary target for the second bomb. The pilots decided to move on to the the secondary target, Nagasaki, after heavy haze hindered their appoach to Kokura. If this author's thesis is correct then the fire bombings of German cities were also intended to kill a maximum number of Christians. His thesis also neglects to explain why Tokyo was fire bombed to such great effect. Truman had no hidden agenda. His intention was to end the war at the earliest possible date.
My source for this information is Samuel J. Walker's Prompt and Utter Destruction. University of North Carolina Press, 1997
I do understand the rationale for the bombings, but it still does not preclude other more strategic targets.