John Connett is one of the most prolific composers of short palindromic phrases. These often come in related families, as shown most spectacularly in "Ed's Palindromic Trickery" in the May 2000 Word Ways. Here are a number of further examples.
Connett, John E.
"Theme and Variations,"
Word Ways: Vol. 34
, Article 20.
Available at: https://digitalcommons.butler.edu/wordways/vol34/iss1/20