11 tricks on a simple squeeze

We arrived in 3NT with East having overcalled one spade. Lefty led spade 2. At a later point when he got in, he exited S9. In the ending, I was able to simple-squeeze East in clubs and spade 8 positionally. But my partner whom I showed the deal, made a fine observation. "You could also have played the S8 on the third round of the suit and made an 11th trick that way. West was very unlikely to hold the ST, or he would have led it if he had the ST9x." It is interersting what inferences there are if we all slow down just a bit. Indeed the club 9 as a menace worked only because East was kind enough to hold all the high clubs.