Besides his own songs, Tom Lehrer had a hand in popularizing (and in one case improving) at least two of the other satirical songs of the late 1950's. He performed Sheldon Harnick's "Merry Little Minuet" at a bill shared with The Kingston Trio in 1958 and they went on to include it on their second album (it had previously been only on Charlotte Rae's Songs I Taught My Mother lp.) Somewhere along the way, it lost the "Little" in the title, an introduction, and mention of Siberia and Switzerland, all of which are on Harnick's recording on DRG.
Tom Lehrer also performer the Pober-Freeman "Gunslinger" in a bill shared with the Limeliters, and they went on to record it. It originally (as on Katie Lee's Songs of Couch and Consultation) had a repeated line. Lehrer improved the song by changing the second (repeated) line to "Did you come from a broken...home on the range?"