Here's a mini-quiz: You have just one stopper in a very short suit and are pretty sure you know which is the dangerous hand here. What do you do under these circumstances:
1. You need take a finesse into each hand. Into which hand first?
2. You need to knock out an ace and finesse into the dangerous hand. Which comes first?
3. You need to knock out an ace and finesse into the non-dangerous hand. Which comes first?
4. You are must knock out two aces. The opponents did not bid. Which comes first?
The answers are: (1) Finesse into the dangerous hand first. You can handle one more attack on that suit, and hope the other hand will be exhausted of that suit if the second finesse loses.
(2) Finesse into the dangerous hand. If that hand knocks out your last stopper, you at least have the hope that the ace lies with the other hand.
(3) Knock out the ace first. You hope that the finesse into the non-dangerous hand works or that that hand is out of your short suit.
(4) That's a trick question. If the two aces are in the same hand, it doesn't matter which you hit first. Only if they're split does it matter, and there's no way of knowing which one has which ace. But if you guess wrong, your partner might be pleased to tell you how you could have known to do otherwise.