Morton & Hayes, on CBS
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This ran from July 24 to August 28, 1991.

For some time now, I've been trying to remember the name of this show... I remembered the basic premise, and I was pretty sure it was aired after some new show that was something of a throwback... my best guesses were either 704 Hauser or Sunday Dinner, both of which were made by Norman Lear, who was perhaps most famous for All in the Family, in the 70s. My confusion is presumably because earlier the same summer that this premiered, "Sunday Dinner" premiered, paired with reruns of "All in the Family." As it turns out, the show this was paired with was reruns of the 1982 series Police Squad!.

Anyway... "Morton & Hayes" was presented (by host Rob Reiner) as newly "rediscovered" short films by a 1930s/40s comedy duo, similar to Abbott & Costello. However, it was actually brand new, but made to look old-fashioned. It was kind of an homage to old comedy short films of that era. I don't remember anything specific about any of the installments, including whether I actually liked the show or not. However, I always kinda liked the concept. I'd really like to see the show again someday, though I doubt that'll happen. Meanwhile, I'm just glad I've finally figured out what the show was. One less thing nagging at the back of my brain periodically, driving me crazy.