She has released albums and fronted bands across varied genres, including contemporary classical, electronic music, pop, art rock, punk, and avant-garde jazz.

She was awarded the 2012 Carl von Ossietsky Composition Prize for Storm, a choral setting of Psalm 104 featuring Brazelton's own retranslation.

"[8] In 1991, she founded and toured with the American chamber music ensemble Bog Life, with musicians John Uehlein, Libby Van Cleve, Elizabeth Panzer, Chris Nappi, Jay Elfenbein, and Ed Broms.

In 2001, Harvestworks, with funding from NYSCA, commissioned Bat to write a 30 minute piece, which became 5 Dreams; Marriage, a set of operatic arias based on Naphtali's wedding vows.

[11] Bat was described by composer John Zorn as "twisted, powerful chamber rock blending a raucous punk aesthetic with vocal harmonies...complex, visionary".

[13] Sleeping Out of Doors, Brazelton's concerto for piano and orchestra, was commissioned and premiered in 1998 by Kristjan Järvi and the Absolute Ensemble, and received a grant from the American Music Center and the Margaret Jory CAP.

Frank Oteri wrote of her: "Brazelton, like many of these new composers, is a composer-performer, and equally at home writing a string quartet or playing in a punk rock band.