This one's new to me: https://www.avclub.com/romania-asked-peter-falk-to-help-prevent-an-uprising-af-1847093587
To the story's "Falk unbelievably asks Letterman, “Was that a good story?”, it is clear that Letterman was about to dispense with the segment, and Falk came it at just the right moment. I never "got" Letterman -- and always felt he was an interrupter and liked to dig for dirt... I thought THIS is what TV's come to? Anyway, great story. Hope it's new to some others here.