Craig Gannon is a British guitarist. He is best known as the rhythm guitarist of The Smiths.
Gannon was hired in early 1986 to replace bassist Andy Rourke, who had been fired from The Smiths for his heroin addiction. After Rourke's return a fortnight later, Gannon moved to playing rhythm guitar. He worked on the singles Panic and Ask, and the scrapped track You Just Haven't Earned It Yet, Baby (which would eventually be compiled in The World Won't Listen.) Gannon served this role during tours to the United Kingdom, Canada and the United States in 1986. After the end of the tour in 1986, Gannon ceased to be part of The Smiths and has since been known as the "Fifth Smith".
Gannon was reunited with former Smiths singer Morrissey at his debut solo gig and 1989 singles "The Last of the Famous International Playboys" and "Interesting Drug". That same year saw him sue Morrissey and Johnny Marr over the degree of his involvement in songwriting (notably for "Ask"). The matter was settled out of court for the sum of £48,000. However, this payment was actually for £30,000 which covered unpaid wages, the remaining £18,000 being legal costs.