The second approach is to figure out the core of the story. If you have 30 seconds to make an elevator pitch, you pull the (alleged) Mark Twain, "baby shoes for sale; never worn" trick of using the fewest words in the most impactful way. Sometimes this is figuring out a quick set-up and pay-off one-two punch in the story.
This is harder, IMO, because it requires that you have thought significantly about your story before you tell it. But I've also found that the more you practice this, the easier it gets to tell a short version and a long version, depending on how the room reads and how the conversations go.
The third way is riskier, but effectively, you play the punch line first. "Once I sang karaoke with Kelly Clarkson at a diner in Mexico City" is a headline statement that makes people say "Wait, WHAT?!" If time is tight, they'll take that one statement and that's good enough to make you interesting. Conversation over. Move along.
But if there's more time or the conversation is able to slow down, you'll have the opportunity to expand it into that larger story. In short, grab their attention with an impactful but ultimately throwaway statement, then reel them in for the long version.