Mainstream success (1993–1995

After the release of a first single, "Dreams" in September 1992, The Cranberries proposed their debut album, Everybody Else Is Doing It, So Why Can't We?, in March 1993. Neither the album nor the single gained much attention, nor did a second single, "Linger". When the band embarked on a tour supporting Suede, they then caught the attention of MTV, which put their videos into heavy rotation. Although "Linger" was first released in the UK in February 1993, peaking at 74, it was later re-issued in February 1994 peaking at 14. This was followed by Dreams (released again in May 1994, peaking at No. 27) which helped their debut album to reach No. 1 on the UK Album Chart,becoming one of only five artists to ever achieve a re-rentry at that chart position. After a North American and European Tour, O'Riordan married the band's tour manager, Don Burton, in July 1994.

O'Riordan's position in the group continued to rise with the fall release of the group's second album, No Need to Argue. Boasting a slightly harder, more streamlined sound, yet still produced byStephen Street, the record debuted at number six on the US charts and eventually outsold its predecessor. Within a year it went triple platinum, spawning the number one hit "Zombie" and the number 11 "Ode to My Family" on the Modern Rock Tracks chart. In 1995, the band continued to tour, and released two more singles "I Can't Be With You" and "Ridiculous Thoughts". The album went 5x platinum in Canada, platinum in Switzerland, and seven times platinum in the United States.