The best replacement for kaye is edward norton.

The best alternatives to kaye are rated as following:
★★★★★  edward norton
★★★★★  james jamerson
★★★  anse chastanet
★★  hal blaine
★★  thomas
★★  george sharp
★  george a sharp

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Speaking about kaye, one probably shouldn't forget about andrews sisters.

Other search terms related to kaye and their ratings are:
★★★★★ andrews sisters
★★★ louis armstrong
andrews sisters)
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kaye
edward norton
james jamerson