I'm not as familiar with her filmed stuff since Youtube availability can be spotty and the only physical media the vast majority of it's been released on is VHS. I'll have to make more of an effort to find torrents or something...
Bill Laswell of Material on bass & production, Anton Fier of the Feelies on drums, Adrian Belew of King Crimson & Talking Heads on guitar, and Daniel Ponce from Herbie Hancock's band on percussion.
Pretty much Laswell's first production gig (alongside Herbie Hancock's "Rockit").
A used copy of the Laurie Anderson debut was the first LP I ever bought (in 1984, on the strength of a Trouser Press record guide mention), and I think "Mister Heartbreak" the second CD I owned.
Course I've guided people to "United States Live" over "Home of the Brave". I'm like that.