The best replacement for burlesque is cabaret.

The best alternatives to burlesque are rated as following:
★★★★★  cabaret
★★★★  vaudeville
★★★  fantasy
★★  boylesque
★  parody
★  coyote ugly

Your alternative for burlesque is not listed? Suggest!
Speaking about burlesque, one probably shouldn't forget about cher and christina.

Other search terms related to burlesque and their ratings are:
★★★★★ cher and christina
You have in mind a companion for burlesque and it is not yet here? Propose!



Google Trends

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burlesque
cabaret
vaudeville