"My Completeness" was the second single released from Thirsty Merc's debut album Thirsty Merc. Reaching number two on the Australian Airplay Chart, the single was the most successful single for the band at the time of its release. It performed considerably better than predecessor, Emancipate Myself, peaking at #27 on the Australian Singles Chart, while highlighting the musical depth and sincerity of the band that secured them a reputation as one of the world's premier alternative acts.