Playing dark, moody pop music that suggests My Bloody Valentine gone garage rock, Gliss learned the hard way that less is more when the first lineup of the group split up. Los Angeles natives Martin Klingman and David Reiss, who traded off on bass and guitar, were disappointed when the other two members of Gliss walked out on them in 2003 after several years of uphill struggle, and they set out to replace them and resume work as a quartet. However, after meeting Victoria Cecilia, an expatriate of Denmark who could play drums, guitar, bass, and keys with equal skill, Klingman and Reiss started rethinking the group's formula, and soon they were playing out as a three-piece in 2004. The new strategy agreed with Gliss, and soon the group was winning new fans both at home and abroad; they found themselves sharing bills with Black Rebel Motorcycle Club, We Are Scientists, Silversun Pickups, and Youth Group, and a visit to the U.K. led to them recording a single for the Mountain Low-Fi label in the summer of 2005. Gliss recorded a cover of Smashing Pumpkins' "Rhinoceros" for a tribute compilation coordinated by MySpace, and discovered the admiration was mutual when Billy Corgan invited the group to open for him on a European tour to promote his first solo album in 2005 (they later opened some dates on Smashing Pumpkins' 2007 reunion tour). Tough Cookie, a British label specializing in digital-only releases, partnered with the band for a series of singles in 2005 and released their first full-length album, Love the Virgins, the following year, as well as an EP, Kissing the Boulevard; in the United States, Gliss signed with Cordless Recordings, a digital label operated under the Warner Bros. banner.