I saw Waits open for Zappa. IIRC, it was at Avery Fisher Hall (or was it still Philharmonic Hall then?). The week before (or after), I saw Zappa at Brooklyn College, with Kathy Dalton opening. Same logic for both: Dalton was on DiscReet, and Waits was managed by Herbie Cohen. Waits appeared solo, and didn't make much of an impression on the audience, who were pretty hardcore Zappa fans. But Waits was still in his Sinatra phase; if he did more of his Beefheart thing, he might have garnered more attention.
I was never a fan of later Waits; he lost me after Nighthawks At The Diner. By far, my favorite album of his was The Heart of Saturday Night; I could listen to that all day.
I still say there's a great untold story of the relationship between Cohen and Zappa. What congruence was there between the Greenwich Village folkie scene and L.A. dada? It probably would have been better if the folkies were never on Straight or DiscReet, as their releases went nowhere.