Playing IMPS in a practice match, you pick up Ax Ax xxx AKJTxx Vul vs Not and hear it go 2H* on your left, P P to you. 2H is a weak 2 suiter with Hearts and another unknown 5 card suit.
I think the main options on this hand are Double, 3C, and 2 or 3NT. I could not bid 4C since that was leaping Michaels and would show a strong 2 suiter in Spades and Clubs. The first 2 bids I rejected since Double I just thought would get me into trouble in Spades. If partner bid any number of Spades, I would have to bypass 3N to bid Clubs, or decide if I was going to bid over 4S, knowing my hand is going to be a disappointment to partner. And 3C would be passed out on many hands where I could make game. The Clubs missing rated to be on me right, since I assumed that the second suit for the 2H bidder was most likely Spades or Diamonds. 2C might very well be right, and probably would be if we were best suited for 5 or even 6 Clubs, but that is about the only time it would be right, and a lot of hands where we can make 5C are going to be passed out in 3C.
This left the 2N and 3N choices. I had a source of tricks and stoppers in 2/3 of the remaining suits, including the primary known suit, so lots of upside on the hand. But the 3 little Diamonds are a large worry, since it was just as likely for the 2H opener to have either of those 2 suits. If Spades, I had little worry, since partner would rate to have Diamonds now. If it was Diamonds, I might not have a stopper in that suit at all. The big questions is what does justice to your hand. You are worth 7 1/2 playing tricks, the A of Diamonds or a stopper and 1 other card will give you at least some play for 9 tricks. So does 2N cover it, or do you have to bid 3N?
The plus for 2N is that partner can show a suit over it, but will you be able to judge where to play the hand when it goes 2H P P 2N P 3S P ?, you have essentially delayed your decision between 3N and 4C for 1 round. The big advantage here is that bidding 4C after 2N describes your hand, it just takes you past 3N :)
The plus for 3N is it makes for a blind lead that may allow you to make a hand you are not entitled to. The down side, it may be a hopeless wrong contract.
At the table I finally decided on 3N. Partner put down not the hoped for dummy with KJxxx KQx x xxxx after the opening Diamond lead. The opps quickly cashed 5 Diamonds winners and exited a Heart. This looked pretty bleak since it appeared 6C was odds on (not sure how you get there) whereas 3N was down 1 on the opening lead. Except when a Club was led from dummy, RHO showed out, LHO was 0553, meaning 6C had 2 losers. Of course this also meant I was down 1 more trick, but that was mostly OK. I thought the only makeable contract was now 5C, kind of hard to get to.
Turns out the other table got to 4S, and made it. Not sure how that worked, and did not ask. Seems like there are only 8, maybe 9 tricks there, with the foul splits. But that is a discussion for another day. And I still think I would bid 3N given another chance, although that 2N-4C auction would sure work well on this hand :)