Blue Gray Gnatcatchers (Polioptila caerulea) flit around in the Palo Verde and Mesquite scrub North of Phoenix. Their sounds are very quiet and unmusical, but they apparently do the job.
The Black-Tailed Gnatcatcher (Polioptila melanura) is a common inhabitant of the desert scrub - you'll find them where you find the Verdin and Black-throated sparrows, both of which were present when I recorded these!