Contestants would be given a punchline and must backfill a joke that uses it. It need not be the original joke that accompanied the punchline, but it must be funny enough for the audience to vote their approval. The first contestant to buzz in after the punchline is read gets to take center stage and
tell the joke. If the audience votes "thumbs down", the punchline is repeated and the other contestants are given a chance to buzz in.
Play would go something like this:
[Host] The Punchline is: (faking a Polish accent) "Ja, of course! But how did you know my name is Walter?"
[Contestant 1] "A man is sitting in a bar watching the pole-vaulting event in the Summer Olympics on TV. He turns to the man next to him and says, (faking a Polish accent) 'That's nothing. In my country I vaulted twice that high and still couldn't make the team.' The other man says, 'Oh, you're a pole vaulter?'"
The Punchlines would get progressively harder through the rounds, e.g. "And the man says, 'Ah ha!'"
I'm still not sure whether or not the audience should be allowed to hear the punchline as it is read to the contestants.